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This book is different from all other books on Life Insurance by at least one of the following characteristics 1-4. 1. The treatment of life insurances at three different levels: time-capital, present value and price level. We call time-capital any distribution of a capital over time: (*) is the time-capital with amounts Cl, ~, ... , C at moments Tl, T , ..• , T resp. N 2 N For instance, let (x) be a life at instant 0 with future lifetime X. Then the whole oO oO life insurance A is the time-capital (I,X). The whole life annuity ä is the x x time-capital (1,0) + (1,1) + (1,2) + ... + (I,'X), where 'X is the integer part ofX. The present value at 0 of time-capital (*) is the random variable T1 T TN Cl V + ~ v , + ... + CNV . (**) In particular, the present value ofA 00 and ä 00 is x x 0 0 2 A = ~ and ä = 1 + v + v + ... + v'X resp. x x The price (or premium) of a time-capital is the expectation of its present value. In particular, the price ofA 00 and äx 00 is x 2 A = E(~) and ä = E(I + v + v + ... + v'X) resp.

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Although there are many books on mathematical finance, few deal with the statistical aspects of modern data analysis as applied to financial problems. This book fills this gap by addressing some of the most challenging issues facing any financial engineer. It shows how sophisticated mathematics and modern statistical techniques can be used in concrete financial problems. Concerns of risk management are addressed by the control of extreme values, the fitting of distributions with heavy tails, the computation of values at risk (VaR), and other measures of risk. Data description techniques such as principal component analysis (PCA), smoothing, and regression are applied to the construction of yield and forward curve. Nonparametric estimation and nonlinear filtering are used for option pricing and earnings prediction. The book is intended for undergraduate students majoring in financial engineering, or graduate students in a Master in finance or MBA program. Because it was designed as a teaching vehicle, it is sprinkled with practical examples using market data, and each chapter ends with exercises. Practical examples are solved in the computing environment of S-PLUS. They illustrate problems occurring in the commodity and energy markets, the fixed income markets as well as the equity markets, and even some new emerging markets like the weather markets. The book can help quantitative analysts by guiding them through the details of statistical model estimation and implementation. It will also be of interest to researchers wishing to manipulate financial data, implement abstract concepts, and test mathematical theories, especially by addressing practical issues that are often neglected in the presentation of the theory. Rene Carmona is the Paul M. Wythes '55 Professor of Engineering and Finance at Princeton University in the department of Operations Research and Financial Engineering and Director of Graduate Studies of the Bendheim Center for Finance. His publications include over seventy articles and six books in probability and statistics. He was elected Fellow of the Institute of Mathematical Statistics in 1984, and he is on the editorial board of several peer-reviewed journals and book series. Professor Carmona has developed computer programs for teaching of statistics, for research in signal analysis, and more recently, he contributed the library EVANESCE for the analysis of heavy tail distributions and copulas. The latter was included in the latest version of S-Plus. He has worked for many years on energy and weather derivatives, and he is recognized as a leading researcher and consultant in this area.

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