March 2013
Monthly Archive
March 27, 2013
I have gone through the book so that I can understand the application of compound Poisson process model and the estimation of relevant parameters. The book, as is evident from the title, talks about the math in insurance context. I like "One example" books where a single example is explored in all dimensions throughout the book. This is one such book where the data relating to “Danish fire insurance” is used to illustrate various modeling principles. This dataset comprises the claim arrivals and claim sizes of a fire insurance firm between 1980 and 1990. The book is rich in visuals and that’s a real nice thing about this book.
There are 4 parts to the book. The first two parts of the book do not need any major fundas other than basic probability and undergrad math. The third part of the book is about generalizing the first two parts of the book using Point processes. I tried going over Point processes without going through the first two parts of the book. However I realized, soon enough, that reading about point processes with a specific example in mind, is a better way and hence read the book in a sequential manner. In this review, I will try to summarize the first two parts of the book.
Part I – Collective Risk Models
Chapter 1: The Basic Model
The basic problem dealt in the book is:
Claims arrive at an insurance firm with claim sizes. One needs to determine the premium that needs to be charged to the customers?
It was Swedish actuary Filip Lundberg(1903) who laid the foundations to nonlife insurance mathematics by introducing a simple model. The key assumptions of this model are claim interarrivals are exponential; claim size sequence is an iid sequence that is independent of the claim arrival process. By specifying the claim interarrival distribution, a counting process also gets specified. This counting process is generally called claim number process.
The main object of interest is the total claim amount process or aggregate claim amount process.
The process S(t) is called the random partial sum process or compound sum process with Ti denoting arrival times, Xi denoting the claim sizes ad N(t) the arrival counting process.
This chapter is a sort of trailer to the book and gives the following list of questions that Part I of the book explores:

Find sufficiently simple probabilistic models for S(t) and N(t),i.e. ways to specify claim size process and claim arrival process

Determine the theoretical properties of the stochastic processes S and N. Distributions of S and N, their distributional characteristics such as the moments, the variance and the dependence structure. Asymptotic properties of N(t) and S(t).

Simulation procedures for N and S

Based on the theoretical properties of N and S, give advice on, How to choose a premium in order to cover the claims in the portfolio? How to build reserves? and How to price insurance products ?
Chapter 2: Models for the Claim Number Process
For the total claim amount process, one needs to assume a process for N(t). This chapter introduces three types of processes that can be used as claim counting process. They are Poisson processes, Renewal processes and Mixture Poisson processes.
Poisson Processes
I think one must kind of be comfortable with viewing three views of claims process, i.e. as an arrival process, as a renewal process and as a counting process. Once you start moving amongst these three views, lot of things are easier to understand. The chapter starts off with standard homogeneous Poisson process, lists various appealing properties of the process and derives them. It then moves on to homogeneous Poisson process and does the same. I think the most important word that I learnt from this chapter is “clocktime”. It is a nice word/analogy for looking at intensity function. Using the terminology of “clocktime”, I understood difference between homogeneous Poisson process and non homogeneous Poisson process. Visualizing the Poisson random measure as an inner clock or operational time of the counting process also helps in simulating an inhomogeneous Poisson process from a homogeneous Poisson process.
The various characteristics of Poisson processes given in this chapter are

Markov property of Homogeneous Poisson process

Backward Recurrence time and Forward recurrence time distributions(useful in understanding inspection paradox)

Joint Distribution of interarrival times

Joint Distribution of the arrival times

Conditional distribution of the arrival times given the number of arrivals – Order statistics property. This amazing property helps in solving a lot of problems where one can substitute order statistics and get a far simpler expression for moment calculations of a random variable that is a function of arrival times. They are many business critical random variables that are functions of arrival times. Delay in claim settlement is one such example.

Distribution of a symmetric function of arrival times
There is a good analysis of Danish fire insurance dataset that illustrates the following points

Estimate the rate parameter of the process using MLE and compare the rate parameter in various years/time intervals

If the intensity varies across years, it is better to fit a local intensity function for each year

A nice way to check whether Poisson process is an approximate model is to transform the process in to standard homogenous Poisson process and visualize the inter arrivals using qqPlot. ‘car’ package in R has a nice function that gives qqPlot for exponential random variable.

Poisson process with constant intensity might be a suitable model for shorter time periods
The first section on Poisson processes ends with an informal discussion of transformed Poisson process and Generalized Poisson processes. This is a good prelude to part III of the book where such things are discussed in a general point process setting. The basic idea is that you want to combine the arrival times and claim size random variables in to one Poisson process.
Renewal Processes
If you generalize a Poisson process allowing arbitrary distribution for interrenewals, you get a renewal process. This generalization has one downside. You do not get closed form expressions like that of a Poisson process. In any case, there is a ton of research that has already been done on Renewals that you can use to analyze the renewal claim arrival process. A brief recap of renewal process theorems are given such as Strong law of large numbers for Renewal processes, Elementary Renewal theorem, CLT for renewal process, Blackwell’s Renewal theorem, Smith’s key renewal theorem. Also a basic intro to renewal equation and solution to the same is given. Based on these fundas, you can test out whatever interrenewal distribution you have in mind, fit it to the data and then use the renewal process theorems to talk about various aspects of the process such as emsemble average, time average, moments such as mean and variance etc.
The Mixed Poisson Processes
Inclusion of mixing variable to the intensity function makes a process Mixed Poisson. The mixed Poisson process inherits the following properties of the Poisson process
The mixed Poisson process loses the following properties of the Poisson process
Chapter 3: The Total Claim Amount
This chapter deals with Xi, the random variable denoting the claim size. It starts off with deriving some rough approximations for premium size calculations.
For a Poisson process, the mean and variance of the total claim process can be obtained in a compact form. For a renewal counting process, one needs to appeal to asymptotics to obtain expressions for the mean and variance of total claim process. SLLN and CLT of Renewal processes help in getting in some grasp on the moments. Why bother about the mean and variance of the total claim process in an asymptotic sense ? The reason being, that these give a clue on premium pricing. For example the expressions for S(t)/t shows that the premium process should be linear function of time. Using mean and standard deviation of the total claim amount process, various types of premiums can be charged.

Premium based on Net Equivalence principle

Premium based on Expected value principle

Premium based on Variance principle

Premium based on Standard deviation principle
Out of the four thumb rules, the premium based on standard deviation principle fits the theoretical requirements.
The second section of this chapter deals with claim size distribution. This section has to do with stat fundas like choosing a right distribution for claim sizes, checking whether the chosen distribution fits the data etc. One often hears about fattailed distributions in many areas and especially in finance. How does one go about measuring it? Let’s say you are given an arbitrary distribution. How do you decide whether it is fat tailed or not? How do you decide analytically? There is no standard answer but one of the ways is to see how the tails behave with respect to the exponential distribution. The following expressions can be used to check whether the distribution is light tailed or fat tailed.
The section introduced a graphical tool called “Mean Excess Plots” that can serve as a guide to check the fat tail presence of the claim sizes. The standard light tailed distributions that once can use are Exponential, Gamma, Weibull, Truncated Normal. It mentions a list of fat tailed distributions, some of which were totally unfamiliar to me. I had never heard of them. The author also gives a note of caution that it is not easy to distinguish between the distributions based on parameter estimation(MLE).Sometimes I wonder why not choose a decent prior and keep updating the claim size distribution, instead of dealing these complex fat tailed distribution functions that anyway are hard to distinguish.
The last section deals with the distribution of the total claim amount under the standard assumption that the claim number process and claim size are independent. Some appealing properties of compound Poisson process are derived. One of them being that sums of independent compound Poisson variables is a compound Poisson variable. A useful tool to cull out a mixture distribution is the characteristic function. A few examples are shown in the context of compound Poisson variable. Three approximation techniques are suggested in the chapter for calculating the total claim amount distribution. First is Panjer recursion, the second one is based on CLT and the third one based on Monte Carlo/Bootstrapping. All three methods have their own drawbacks.
Chapter 4: Ruin Theory
I felt this chapter to be the most challenging one in the book. It is easy to understand the question the chapter deals with. Given a total claim amount process, what is the probability that a firm goes bankrupt? So, given an initial capital that is used to start an insurance firm, the premium payment process and the claim disbursement process can cause the net amount to hit 0. The solution to ruin probability is complicated. This chapter gives techniques to compute rough approximations to the probability of ruin. These are basically some bounds on the ruin probability and the math used is based on renewal equation. Most of the content deals with the “small claim size” scenario.
Part II – Experience Rating
Chapter 5 & 6: Bayes Estimation + Linear Bayes Estimation
The estimation problem dealt in this chapter is,
How can one determine a premium for a specify policy by taking the claim history of that policy into account?
Two models are introduced, one being a heterogeneity model and the other being a model based on Linear Bayes estimation.The idea of the heterogeneity model is to incorporate a customer specific parameter that captures the individual attributes. One assumes a prior for this parameter, assumes a likelihood model for the data and then updates the prior. So, given the claim history of a customer, one tries to find to reasonable approximation to Expected value of claim size given this heterogeneity parameter. Even though this looks good in theory, the problem is that there is a strong assumption, i.e. conditional on the heterogeneity parameter, the claim sizes are iid. The chapter of Linear Bayes relaxes this condition and states a model with a rather weak assumption.
Takeaway :
Even the context of the book is nonlife insurance, the math relating to counting measures can be applied to variety of areas. For a reader looking for a solid understanding of compound Poisson processes, this book can be a good starting point. The total claim amount process can serve as a good real life example while going over abstract details of point processes.
March 23, 2013
Posted by safeisrisky under
Books,
Programming
Leave a Comment
I stumbled on to RStudio (an open source IDE ) 2 years ago and felt there was a need for a lot of improvement before I could make a switch from eclipse IDE. As I check out the features of it, I see that there has been a ton of improvement in the features. I went through this book to get a basic overview of all features at once. The RStudio site has a set of documentation pages that looks equally good. The only advantage in reading this book is that all the things about RStudio are organized and presented in a systematic manner.
The features that are appealing in RStudio are :

I had come across ipython notebook and loved it as it gave the flexibility of incremental programming. I was happy to see that a similar notebook option has now been introduced in RStudio. You can bunch all your code and the output in one single HTML page. Also there is a site
RPubs where you can share your notebook with others.

Sweave is tightly integrated and is far more pleasant to use than in other IDEs. With very minimal configuration, you can write Sweave documents and convert in to PDF

Came across 2 other modes for creating reproducible research: Markdown language, HTML. The former reminds me of “restructured Text” in Python world. Markdown language is very similar to ReST. So if you know ReST, there is hardly any learning curve for using Markdown language. I think the HTML option of reporting is just a nice to have feature. Frankly I don’t think anyone would really use the option given that there are three other options – Sweave, Notebook and Markdown.

For LaTeX/Sweave, one can always use native Sweave driver but weaving with “knitr” gives far more flexibility. In fact this is the part that is most useful to me. While using native Sweave, I had to figure out all many options by reading Sweave manual, but with knitr, they are all readily available. I am going to switch to weaving via knitr.

The chunk specific functionality is also very useful if one is creating a huge report.

Sync PDF view : Another very useful feature is the toggle feature between Sweave and PDF. I think the first time I came across this kind of feature was in TeXworks. You highlight a chunk and press toggle, you are automatically taken to the relevant part of the PDF. Very useful feature

Roxygen2 support for package documentation

devtools support and github support
This book is useful in the sense that all features of IDE are written in a systematic fashion. If you plan to use RStudio, it might be better to go over this book as there is a high likelihood of stumbling on to features you might want to use. Reading online hyperlinked documentation has a benefit in terms of massive content but it also has a downside it is easy to get lost and miss out the essential features. This book helps you get an overview of all the features with minimal distraction.
March 22, 2013
Posted by safeisrisky under
Books,
Finance
Leave a Comment
I had to vacate my old flat and move to a new apartment recently and hence had to shift all my books. This entailed categorizing all of them to suit the new shelf space. It was quite an effort and I had to take a day off from work to get the task done. In the process, I stumbled on to this book that was lying in my inventory for many years. This book was published way back in 2004 and I bought it sometime in 2007 thinking that it might give me a 10,000 ft. view of Black Scholes. Working on details sometimes might make one miss the forest for the trees. Books such as these, exist to provide intuition behind the option pricing math. Having said that, the math in the book is not dumbed down as title might seem to suggest. I read this book after 6 years of purchase. At this rate, I think I will barely manage to read all the books that I have, by the time I die .
Ok, firstly about the author. An earlier book by Falcon Crack ,”Heard on Street” is a popular book among newbie financial engineers. The book is a collection of interview questions posed to people seeking a junior quant position. This book is not directly targeted towards that kind of audience. It claims to give an intuitive background to BlackScholes and I think in that aspect, it does a fair job. It has “trading” in its title and I think it is grossly misleading. There is a chapter on trading but it could as well have been pushed to the appendix.
What I liked about the book ?

Put call parity explained through a visual that shows the relationship between intrinsic and extrinsic value of call options. The fact that you also get to see put option pricing dynamics in the same visual makes it very appealing. This explanation gives the much needed intuition in order to grasp the Black Scholes formula

Single summary table that explains the effect of strike price, time value, interest rate, volatility, underlying price, dividends on the call and put option values.

Trivia – European Vs. American Option – Why are they named that way ?: Paul Samuelson at MIT said that he carefully chose the names “European” and “American” (back in 1960s), as he wanted to take a swipe at snobby European economists who thought themselves more sophisticated than their American counterparts. Samuelson did this by naming the more sophisticated exercise style as “American” and the less sophisticated as “European”

Nice argument that verbalizes the reason for the absence of “PutCall Parity” type of equation for American options.

Why is the value of the option, not a function of risk preferences? – Intuitive explanation as to why a quant lives in a risk neutral world for pricing options.

Derivation of Black Scholes using various approaches and a nice explanation of various terms in the Black Scholes pricing formula.

Provides good intuition about option greeks.
There are some things that are not so pleasant about the book. But I don’t want to waste time writing about them. Already the author has wasted his time writing them in the first place.
The book is easy on eyes and can be easily read from cover to cover in one sitting. Since this book goes one level deeper than the MBAish books like Hull, it might be a good supplement to such books.
March 16, 2013
The principles of Renewal theory are seen in various stochastic processes such as Countable State Markov chains, Continuous Markov processes, SemiMarkov processes, Regenerative processes etc. In one sense, spotting a Renewal process in a complicated stochastic process makes life easy as one can use the concepts from renewal theory to talk about the ensemble average and limiting time averages of the process. This book belongs to the “classics” genre of Renewal theory. Let me attempt to summarize the main chapters of the book.
Chapter 1: Preliminaries
Renewal theory began as the study of some particular probability problems connected with the failure and replacement of components, such as electric light bulbs. Later it became clear that some of the same problems arise also in connection with many other applications of probability theory. The main random variable is X, the failure time. Actually you can think of X as any process that registers a new arrival epoch. The random variable can be discrete or continuous. The book by Feller covers the discrete case and this book is all about continuous case. One of the essential tools to analyze Renewals is “Laplace Transform”. One has to get friendly with Laplace and Inverse Laplace transforms to derived closed form solutions for specific distributions. The three most common distributions used in the book are Exponential, Special Erlangian and Gamma. Why restrict to only these? Well, for one thing, in order to get some insight in to the theory, you work with distributions that have closed form solutions. Secondly, all said and done, the renewal processes with interrenewal distributions as exponential or gamma are one of the widely studied and applied stochastic processes. To think about it, what’s the point in trying in introducing a theory that has complicated interrenewal distribution?.
Chapter 2: Fundamental Models
This chapter defines three processes associated with a Renewal process, i.e. inter renewal sequence of IIDS, the renewal epoch sequence and the renewal counting process. All the three describe the same system. It’s like giving three different views to the same process. For example if you take a simple Poisson arrival process where the counting process has a poisson random measure, the interarrival sequence is exponential, the renewal epoch sequence is special erlangian. It is fairly important to switch from one sequence to another at regular intervals so that you can see what’s going on in the process, as well as compute various statistics of interest.
The chapter talks about three types of Renewal processes

Ordinary Renewal process : First failure time has the same distribution as the subsequent failure times

Modified Renewal process / Delayed Renewal process : First failure time has a different distribution than that of subsequence failure times

Equilibrium Renewal process: First failure time has a specific form of distribution that gives nice asymptotic results.
Delayed renewal process is different from Ordinary renewal process in the assumption about the first renewal. In the ordinary renewal process, the first renewal occurs at time 0. In delayed renewal, the first renewal can have any distribution.
Having defined the process, the chapter lists the most common random variables that one needs to get a handle on, to understand any renewal process

Time up to rth renewal.

Number of renewals in time t (Nt).

The renewal function.

Renewal density – Although it is technically not a density.

Higher moments of Nt like expectation and variance.

Backward recurrence time (Age).

Forward recurrence time ( Residual life).
To give a taste of things to come in the book, all the above aspects are derived for a renewal process with interrenewal times as exponential.
Chapter 3: Distribution of Renewals
This chapter derives the distribution of renewals, i.e. distribution of counting process and distribution of renewal epochs. Since they describe the same system, one can switch between two sequences from time to time to get the distribution of both the processes. Also the approach taken here shows the power of Laplace transforms, i.e. start off with a probability generating function, apply Laplace transform to get an expression that involves Laplace transform of the interrenewal density function. The resulting expression is an equation between Laplace transform of the generating function of counting process and Laplace transform of the interrenewal density function. This expression is generic in the sense that you can plug in LT of any interrenewal distribution and you obtain the LT of renewal counting. All you have to do is to take inverse LT of the expression to get the distribution of renewals. So, the key takeaway is the generic expression of renewal distribution that involves LT of interrenewal density. These expressions are used throughout the book. In fact the LT of generating functions of all the three types of renewal processes, i.e. Ordinary renewal, Modified renewal and Equilibrium renewal processes are derived. The chapter ends with a Central Limit theorem type statement for the number of renewals in time t.
Chapter 4: Moments of Number of Renewals
The recipe is the same as the previous chapter. Start off with the generating function for the whatever moment you are interested in, E(X^r), take the Laplace transform, get it to a form that involves Laplace transform of the interrenewal distribution, and then take inverse Laplace to get the moment function. In the context of Renewal theory, the first moment has a special name called “Renewal function”. In fact a ton of problems are solved using a specific form involving renewal function, called the “Renewal equation”. This chapter derives the first moment and the second moment for all the three types of renewal processes, i.e. ordinary+delayed+equilibrium processes.
Although renewal equation is not dealt much in this book, there are a range of problems that can be solved using Renewal equation. The basic funda behind renewal equation is that you get a recurrence relation in discrete or continuous time after conditioning on the first renewal.
Chapter 5: Recurrence Times
In any renewal process, there are some basic questions that are of interest? When is the next renewal going to happen? If I land up at a particular time, what is the time since the last renewal? The former is called the residual life and the latter is the called the age. Both of these are random variables can be formulated using Renewal Reward theory and the distribution of both these variables can be computed. However this book does not use Renewal Reward theory, but builds up on the theory introduced in previous chapters, ie. use Laplace transforms. Somehow I felt this part could have been easily handled using Renewal reward theory instead of the painfully long computations given in the book.
Chapter 6: Superposition of Renewal Processes
This chapter talks about a process that is a result of more than one renewal processes. The resulting process obviously need not be a renewal process. However by assuming independence of constituents, one can come up with some closed form solutions. There is also a mention of the distribution of the interval between successive renewals. Note that since the resulting process is not a renewal process, the distribution is not always easy to derive.
Chapter 7: Alternating Renewal Processes
This is a relatively easier phenomenon to handle than the superposition case. The resulting process is still a renewal process and hence all the random variables that were derived for a single renewal process can be extended easily to this case. This chapter also gives a gentle introduction to SemiMarkov processes. It is in this chapter that renewal equation is used to solve the probability of the system in a particular state. Again solving a renewal equation is made easy by taking a LT of the entire equation.
Chapter 8: Cumulative Processes
At each of the renewal epochs, one can associate a random variable and there are many situations where one is interested in the cumulative sum of this random variable. Bulk arrivals, Poisson Markings, Poisson thinning etc are all examples of cumulative processes. The distribution and the first passage time for these cumulative processes are explored in this section.
Chapter 9 further generalized the renewal process assumptions. Chapter 10 and 11 deal with application of renewal processes to very specific problem areas such as models of failure and replacement strategies, more relevant to manufacturing context.
The core principles of the book are laid out in the first 9 chapters and take up 100 pages. I think it’s better to approach this book after having some decent fundas on Laplace transforms. In fact the cover page of the book illustrates the technique of contour integration that is relevant to obtain inverse Laplace transform. In any case, renewal theory principles are extremely important for someone interested in countable state Markov processes and Continuous time Markov processes.
March 5, 2013
Posted by safeisrisky under
Books,
Learning
1 Comment
The authors are math professors at Princeton. This book is a result of a 7 year effort. It distills all their math teaching experiences in to 150 pages. The book is targeted towards general audience even though most of anecdotes are from a classroom environment.
The authors use the 5 classic Greek elements that were thought to be the foundation of everything – Earth, Fire, Air, Water and Quintessential – to lay out the principles of effective thinking. The authors had approached Princeton university press with a novel idea, i.e., make three copies of the same book and bundle it to one fat book and sell it. The thought process being the book needs to be read at least three times. In the first read, you should read cover to cover to get the big picture of the book. In the second read you are supposed to pause at various points of the book and go over the action items carefully and in the third read, you are to read randomly across various sections and see the connections. The Princeton press with all due respect to the authors rejected their novel idea. So, the book is just about 150 pages but definitely deserves to be read a couple of times to get the best out of it.
The authors give the following connection between 5 classic Greek elements and 5 elements of thinking
Strive for rocksolid understanding
Fail and learn from those missteps
Constantly create and ask challenging questions
Consciously consider the flow of ideas
Learning is a lifelong journey; thus each of us remains a workinprogress— always evolving, ever changing— and that’s Quintessential living.
Well, none of this is something that we have not come across before. We already know all this at some level but this book brings those memories in to the present. Having these principles in working memory, will make us constantly question the way we go about learning, the way we work and the way we apply thinking in our lives.
March 5, 2013
Posted by safeisrisky under
Books,
Reflections
1 Comment
The book is about the conversations the author Will Schwalbe has with his mother while she underwent pancreatic cancer treatment.
Mary Anne, the author’s mother is diagnosed with pancreatic cancer in 2007. For a span of two years she undergoes treatment at a cancer hospital in NY that included long hours of chemotherapy sessions. The author often used to accompany her mother for all her treatments. Most of the doctors give their verdict that the cancer has spread and the various treatments can only delay her eventual death.
During one of the long waits at the hospital, a simple question, “What are you reading?” takes the motherson duo on to a wonderful journey of books for 2 years. The books they read are not are not serious kind books. They read all kinds of books, ranging from classics, teen adventures, poetry, love stories, tragedies, dark theme books and then they discuss the characters, the endings, the situations in the novels etc. So, the book club is essentially a 2 person book club where the mother and the son discuss about the books they have read. In the process the author discovers so many aspects of her mother that he never did earlier.
The very first novel they read is “Crossing from Safety” and the discussion is around whether one of the characters in the novel would be able to handle the situation after his loved one’s death. Clearly even though the discussion was about the characters in the book, they were indirectly addressing the aspect of how family members would be able to deal with the death of their mother, who throughout her life gave direction to everyone and was the hub of the family.
“Reading isn’t the opposite of doing; it’s the opposite of dying” is a theme that comes up in many of their discussions. One is not supposed to merely read a book and forget about it. One must constantly question, “What should I be doing to do about the themes mentioned in the book?”. May be you can be compassionate towards people that you encounter in your life, May be you can do just do your bit in addressing the situation, develop a better perspective towards life etc.
One of the reasons, the author gives, about choosing such a title,”The end of YOUR LIFE book club”, You don’t know what book would be your last book, what conversation will be your last conversation. So, it is more “seize the moment” kind of attitude that this book conveys.
Towards the end of the book, the author says this about his mom :
She never wavered in her conviction that books are the most powerful tool in the human arsenal, that reading all kinds of books, in whatever format you choose—electronic (even though that wasn’t for her) or printed, or audio—is the grandest entertainment, and also is how you take part in the human conversation. Mom taught me that you can make a difference in the world and that books really do matter: they’re how we know what we need to do in life, and how we tell others. Mom also showed me, over the course of two years and dozens of books and hundreds of hours in hospitals, that books can be how we get closer to each other, and stay close, even in the case of a mother and son who were very close to each other to begin with, and even after one of them has died.
It is pretty amazing that over a span of two years(20072009), despite starting a company and having a hectic schedule, the author manages to read about 100 odd books.It shows how much he loved her mother. Here is the entire list that are discussed in the book. So, just in case you happen to read any book from this list, you can always look up the relevant section in the book and see what the two member motherson book club had to say about it and what they learnt in the process.
 Louisa May Alcott, Little Women
 Dante Alighieri, Purgatorio
 W. H. Auden, “Musée des Beaux Arts,” from Collected Poems
 Russell Banks, Continental Drift
 Muriel Barbery, The Elegance of the Hedgehog, translated by Alison Anderson
 Ishmael Beah, A Long Way Gone
 Alan Bennett, The Uncommon Reader
 Roberto Bolaño, The Savage Detectives, translated by Natasha Wimmer
 The Book of Common Prayer
 Geraldine Brooks, March; People of the Book
 The Buddha, The Diamond Cutter Sutra, translated by Gelong Thubten Tsultrim
 Lewis Carroll, Alice’s Adventures in Wonderland
 Sindy Cheung, “I Am Sorrow”
 Julia Child, Mastering the Art of French Cooking
 Karen Connelly, The Lizard Cage
 Pat Conroy, The Great Santini
 Roald Dahl, Charlie and the Chocolate Factory
 Patrick Dennis, Auntie Mame
 Joan Didion, A Book of Common Prayer; The Year of Magical Thinking
 T. S. Eliot, Murder in the Cathedral
 Ian Fleming, Chitty Chitty Bang Bang
 Ken Follett, The Pillars of the Earth
 Esther Forbes, Paul Revere and the World He Lived In; Johnny Tremain
 E. M. Forster, Howards End
 Anne Frank, Anne Frank: The Diary of a Young Girl
 William Golding, Lord of the Flies
 Günter Grass, The Tin Drum
 David Halberstam, The Coldest Winter
 Susan Halpern, The Etiquette of Illness
 Mohsin Hamid, The Reluctant Fundamentalist
 Patricia Highsmith, Strangers on a Train; The Price of Salt; The Talented Mr. Ripley
 Khaled Hosseini, The Kite Runner; A Thousand Splendid Suns
 Henrik Ibsen, Hedda Gabler
 John Irving, A Prayer for Owen Meany
 Christopher Isherwood, The Berlin Stories; Christopher and His Kind
 Jerome K. Jerome, Three Men in a Boat
 Ben Johnson, Volpone
 Crockett Johnson, Harold and the Purple Crayon
 Erica Jong, Fear of Flying
 Jon Kabat Zinn, Full Catastrophe Living; Wherever You Go, There You Are; Coming to Our Senses
 Mariatu Kamara, The Bite of the Mango, with Susan McClelland
 John F. Kennedy, Profi les in Courage
 Jhumpa Lahiri, Interpreter of Maladies; The Namesake; Unaccustomed Earth
 Anne Lamott, Traveling Mercies
 Stieg Larsson, The Girl with the Dragon Tattoo, translated by Reg Keeland
 Victor LaValle, Big Machine
 Munro Leaf, The Story of Ferdinand, illustrated by Robert Lawson
 C. S. Lewis, The Chronicles of Narnia
 Alistair MacLean, The Guns of Navarone; Where Eagles Dare; Force 10 from Navarone; Puppet on a Chain
 Malcolm X, The Autobiography of Malcolm X: As Told to Alex Haley
 Thomas Mann, Tonio Kröger; Death in Venice; The Magic Mountain;Mario and the Magician; Joseph and His Brothers,
 W. Somerset Maugham, Of Human Bondage; The Painted Veil;Collected Short Stories, including “The Verger”
 James McBride, The Color of Water
 Ian McEwan, On Chesil Beach
 Herman Melville, Billy Budd
 Arthur Miller, Death of a Salesman
 Rohinton Mistry, A Fine Balance
 Margaret Mitchell, Gone With the Wind
 J. R. Moehringer, The Tender Bar
 Daniyal Mueenuddin, In Other Rooms, Other Wonders
 Alice Munro, Too Much Happiness
 Nagarjuna, Seventy Verses on Emptiness, translated by Gareth Sparham
 Irène Némirovsky, Suite Française, translated by Sandra Smith
 Edith Nesbit, The Railway Children
 Barack Obama, Dreams from My Father
 John O’Hara, Appointment in Samarra
 Mary Oliver, Why I Wake Early, including “Where Does the Temple Begin, Where Does It End?”
 Frances Osborne, The Bolter
 Randy Pausch, The Last Lecture, with Jeffrey Zaslow
 Susan Pedersen, Eleanor Rathbone and the Politics of Conscience
 Harold Pinter, The Caretaker
 Reynolds Price, Feasting the Heart
 Arthur Ransome, Swallows and Amazons
 David Reuben, M.D., Everything You Always Wanted to Know About Sex: But Were Afraid to Ask
 David K. Reynolds, A Handbook for Constructive Living
 Marilynne Robinson, Housekeeping; Gilead; Home
 Tim Russert, Big Russ and Me
 Maurice Sendak, Where the Wild Things Are; In the Night Kitchen
 Peter Shaffer; Equus; Five Finger Exercise
 William Shakespeare, King Lear; Othello
 George Bernard Shaw, Saint Joan
 Bernie Siegel, M.D., Love, Medicine and Miracles
 Alexander McCall Smith, The No. 1 Ladies’ Detective Agency: The Miracle at Speedy Motors
 Aleksandr Solzhenitsyn, The Gulag Archipelago
 Natsume Soseki, Kokoro, translated by Edwin McCellan
 Wallace Stegner, Crossing to Safety
 Edward Steichen, The Family of Man
 Lydia Stone, Pink Donkey Brown, illustrated by Mary E. Dwyer
 Elizabeth Strout, Olive Kitteridge
 Josephine Tey, Brat Farrar
 Michael Thomas, Man Gone Down
 Mary Tileston, Daily Strength for Daily Needs
 Colm Tóibín, The Story of the Night; The Blackwater Lightship;The Master; Brooklyn
 J. R. R. Tolkien, The Hobbit; The Lord of the Rings
 William Trevor, Felicia’s Journey
 John Updike, Couples; My Father’s Tears
 Sheila Weller, Girls Like Us
 Elie Wiesel, Night
 Tennesse Williams, A Streetcar Named Desire
 Geoffrey Wolff, The Duke of Deception
 Herman Wouk, The Caine Mutiny; Marjorie Morningstar; The Winds of War