Introductory Stochastic Analysis for Finance and Insurance (Wiley Series in Probability and Statistics)

Book Description

Incorporates the many tools needed for modeling and pricing in finance and insurance

Introductory Stochastic Analysis for Finance and Insurance introduces readers to the topics needed to master and use basic stochastic analysis techniques for mathematical finance. The author presents the theories of stochastic processes and stochastic calculus and provides the necessary tools for modeling and pricing in finance and insurance. Practical in focus, the book's emphasis is on application, intuition, and computation, rather than theory.

Consequently, the text is of interest to graduate students, researchers, and practitioners interested in these areas. While the text is self-contained, an introductory course in probability theory is beneficial to prospective readers.

This book evolved from the author's experience as an instructor and has been thoroughly classroom-tested. Following an introduction, the author sets forth the fundamental information and tools needed by researchers and practitioners working in the financial and insurance industries:
* Overview of Probability Theory
* Discrete-Time stochastic processes
* Continuous-time stochastic processes
* Stochastic calculus: basic topics

The final two chapters, Stochastic Calculus: Advanced Topics and Applications in Insurance, are devoted to more advanced topics. Readers learn the Feynman-Kac formula, the Girsanov's theorem, and complex barrier hitting times distributions. Finally, readers discover how stochastic analysis and principles are applied in practice through two insurance examples: valuation of equity-linked annuities under a stochastic interest rate environment and calculation of reserves for universal life insurance.

Throughout the text, figures and tables are used to help simplify complex theory and pro-cesses. An extensive bibliography opens up additional avenues of research to specialized topics.

Ideal for upper-level undergraduate and graduate students, this text is recommended for one-semester courses in stochastic finance and calculus. It is also recommended as a study guide for professionals taking Causality Actuarial Society (CAS) and Society of Actuaries (SOA) actuarial examinations.

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Incorporates the many tools needed for modeling and pricing in finance and insurance Introductory Stochastic Analysis for Finance and Insurance introduces readers to the topics needed to master and use basic stochastic analysis techniques for mathematical finance. The author presents the theories of stochastic processes and stochastic calculus and provides the necessary tools for modeling and pricing in finance and insurance. Practical in focus, the bok's emphasis is on application, intuition, and computation, rather than theory. Consequently, the text is of interest to graduate students, researchers, and practitioners interested in these areas. While the text is self-contained, an introductory course in probability theory is beneficial to prospective readers. This book evolved from the author's experience as an instructor and has been thoroughly classroom-tested. Following an introduction, the author sets forth the fundamental information and tools needed by researchers and practitioners working in the financial and insurance industries: Overview of Probability Theory Discrete-Time stochastic processes Continuous-time stochastic processes Stochastic calculus: basic topics The final two chapters, Stochastic Calculus: Advanced Topics and Applications in Insurance, are devoted to more advanced topics. Readers learn the Feynman-Kac formula, the Girsanov's theorem, and complex barrier hitting times distributions. Finally, readers discover how stochastic analysis and principles are applied in practice through two insurance examples: valuation of equity-linked annuities under a stochastic interest rate environment and calculation of reserves for universal life insurance. Throughout the text, figures and tables are used to help simplify complex theory and pro-cesses. An extensive bibliography opens up additional avenues of research to specialized topics. Ideal for upper-level undergraduate and graduate students, this text is recommended for one-semester courses in stochastic finance and calculus. It is also recommended as a study guide for professionals taking Causality Actuarial Society (CAS) and Society of Actuaries (SOA) actuarial examinations.

Applied Stochastic Models and Control for Finance and Insurance

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Applied Stochastic Models and Control for Finance and Insurance
Charles S. Tapiero
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0792381483

Book Description

Applied Stochastic Models and Control for Finance and Insurance presents at an introductory level some essential stochastic models applied in economics, finance and insurance. Markov chains, random walks, stochastic differential equations and other stochastic processes are used throughout the book and systematically applied to economic and financial applications. In addition, a dynamic programming framework is used to deal with some basic optimization problems.
The book begins by introducing problems of economics, finance and insurance which involve time, uncertainty and risk. A number of cases are treated in detail, spanning risk management, volatility, memory, the time structure of preferences, interest rates and yields, etc. The second and third chapters provide an introduction to stochastic models and their application. Stochastic differential equations and stochastic calculus are presented in an intuitive manner, and numerous applications and exercises are used to facilitate their understanding and their use in Chapter 3. A number of other processes which are increasingly used in finance and insurance are introduced in Chapter 4. In the fifth chapter, ARCH and GARCH models are presented and their application to modeling volatility is emphasized. An outline of decision-making procedures is presented in Chapter 6. Furthermore, we also introduce the essentials of stochastic dynamic programming and control, and provide first steps for the student who seeks to apply these techniques. Finally, in Chapter 7, numerical techniques and approximations to stochastic processes are examined.
This book can be used in business, economics, financial engineering and decision sciences schools for second year Master's students, as well as in a number of courses widely given in departments of statistics, systems and decision sciences.

Non-Life Insurance Mathematics: An Introduction with Stochastic Processes (Universitext)

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Non-Life Insurance Mathematics: An Introduction with Stochastic Processes (Universitext)
Thomas Mikosch
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 3540406506

Book Description

This book offers a mathematical introduction to non-life insurance and, at the same time, to a multitude of applied stochastic processes. It gives detailed discussions of the fundamental models for claim sizes, claim arrivals, the total claim amount, and their probabilistic properties. Throughout the book the language of stochastic processes is used for describing the dynamics of an insurance portfolio in claim size space and time. In addition to the standard actuarial notions, the reader learns about the basic models of modern non-life insurance mathematics: the Poisson, compound Poisson and renewal processes in collective risk theory and heterogeneity and Bühlmann models in experience rating. The reader gets to know how the underlying probabilistic structures allow one to determine premiums in a portfolio or in an individual policy. Special emphasis is given to the phenomena which are caused by large claims in these models. What makes this book special are more than 100 figures and tables illustrating and visualizing the theory. Every section ends with extensive exercises. They are an integral part of this course since they support the access to the theory. The book can serve either as a text for an undergraduate/graduate course on non-life insurance mathematics or applied stochastic processes. Its content is in agreement with the European "Groupe Consultatif" standards. An extensive bibliography, annotated by various comments sections with references to more advanced relevant literature, make the book broadly and easiliy accessible.

Practical Risk Theory for Actuaries (Monographs on Statistics and Applied Probability)

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Practical Risk Theory for Actuaries (Monographs on Statistics and Applied Probability)
C.D. Daykin , T. Pentikainen , and Martti Pesonen
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0412428504

Stochastic Processes for Insurance and Finance (Wiley Series in Probability and Statistics)

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Stochastic Processes for Insurance and Finance (Wiley Series in Probability and Statistics)
Tomasz Rolski , Hanspeter Schmidli , Volker Schmidt , and Jozef Teugels
Manufacturer: Wiley
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471959251

Book Description

Stochastic Processes for Insurance and Finance offers a thorough yet accessible reference for researchers and practitioners of insurance mathematics. Building on recent and rapid developments in applied probability, the authors describe in general terms models based on Markov processes, martingales and various types of point processes.
Discussing frequently asked insurance questions, the authors present a coherent overview of the subject and specifically address:
· The principal concepts from insurance and finance
· Practical examples with real life data
· Numerical and algorithmic procedures essential for modern insurance practices
Assuming competence in probability calculus, this book will provide a fairly rigorous treatment of insurance risk theory recommended for researchers and students interested in applied probability as well as practitioners of actuarial sciences.

Wiley Series in Probability and Statistics

Measuring Risk in Complex Stochastic Systems

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Discusses interesting alternatives to risk analysis/measurement

Measuring Risk in Complex Stochastic Systems

Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Book Description

This collection of articles by leading researchers will be of interest to people working in the area of mathematical finance.

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Discusses interesting alternatives to risk analysis/measurement.......2006-07-26

The analysis, modeling, and measurement of risk are now a multi-billion dollar industry, employing armies of analysts and risk managers, and frequently making use of highly sophisticated mathematics. This short book is a collection of articles that address some of the main issues in risk management from several different viewpoints, such as credit risk management, extreme value analysis, Value at Risk (VAR), and credit scoring methods. Most of the articles include discussion on how to use the results for real-world applications, or how to validate them for possible use in a financial institution of interest. Readers are expected to have a fairly substantial mathematical background, including of course probability and statistics, especially the theory of stochastic processes, the latter mostly in the guise of Brownian or geometric Brownian motion.

In the article by Ludger Overbeck he compares capital allocation rules that are based on conditional expectation, marginal economic capital, and on covariances in the context of credit portfolios. Taking the ability-to-pay process as being given by multivariate Brownian motion, he assumes first that the default probability for a single customer and the correlation matrix for the ability-to-pay process are known, and then sets out to compute the loss distribution for the case of m customers each with a particular exposure. The exposures are assumed to be non-random and the author first estimates the loss distribution using Monte Carlo simulation. He then gives a quick overview of the economic capital definition for a portfolio in terms of the quantile of the loss distribution, and how to allocate capital throughout the portfolio using Var/Covar. This approach involves the `risk contributions' to the standard deviation. The author calculates the risk contributions explicitly and notes that the difference between the quantile and the mean is a multiple of the standard deviation in the case of the normal distribution. When the distribution is not normal, the author defines the `contributory economic capital (CEC)' as the product of the risk contributions and the economic capital normalized by the standard deviation. This discussion motivates the concept of `marginal economic capital (MEC)', which is the difference between the economic capital of the portfolio and the economic capital of the portfolio without the transaction. The author then notes that the sum of each MEC is not equal to the economic capital, the CEC is then set to be proportional to the MEC. It is at this point where the discussion is the most interesting, for the author brings in the notion of a `coherent risk measure' as a competitor to the approach of risk management by quantiles. Similar to the requirements for a measure in ordinary measure theory, a coherent risk measure must be bounded, subadditive, positively homogeneous, translation invariant, and monotonic. The concept of a coherent risk measure has a fairly extensive literature at the present time, and usually presented in an axiomatic framework with the above requirements to be satisfied. These requirements are well motivated from the standpoint of an intuitive understanding of risk. The boundedness requirement for example is clear (no such thing as infinite risk), whereas the translation invariance implies that the addition of an amount to the portfolio increases the risk measure by this amount. The subadditivity requirement means essentially that the risk of two merged portfolios cannot be greater than the sum of the individual portfolio risks. The requirement of positive homogeneity means that if a portfolio P grows in size by some factor then the risk of this enlarged portfolio is equal to the risk of P multiplied by this factor. The author goes on to define a coherent risk measure and a definition of capital in terms of this measure, namely the economic capital is the expected value of the losses given that the losses are above some selected level. He then compares the different capital allocation methods with real portfolio data and Monte Carlo simulations. The authors use of Monte Carlo simulations requires in some cases a large number of paths, as he points out in the article, this arising mostly from simulating losses and capital allocations to single counterparties (the shortfall contributions being allowed by the capital definition). He recommends future study of these simulations. Perhaps techniques for variance reduction can be of assistance.

The article by Marlene Muller and Bernd Ronz overviews their method of doing credit scoring using semiparametric methods, which is a special method wherein part of the explanatory variables can be modeled nonparametrically. The payoff they say in using this method is that one can find out how the logistic discriminant has to be changed in order to better differentiate between good and bad loans. Such knowledge would definitely be useful, since after a typical discriminant analysis one usually has no idea how to alter the model in order to reduce the resulting error in classification. Explicitly, the Muller-Ronz credit scoring model involves the computation of the conditional expectation of the response variable given the explanatory in terms of a known function of unknown parameters and an unknown nonparametric function, the latter of which can be estimated by a quasilikelihood method. This computation is only advantageous if it outperforms the parametric logit method for credit scoring, and using real data the authors compare their model with the logit method in the article by calculating misclassification and performance curves, and conclude that the semiparametric model improves the performance with respect to the parametric model.

Random Evolutions and their Applications: New Trends (Mathematics and Its Applications)

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Random Evolutions and their Applications: New Trends (Mathematics and Its Applications)
A. Swishchuk
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0792362640

Book Description

This book is devoted to new trends in random evolution and their applications to the stochastic evolutionary system. It contains new developments such as an analogue of Dynkin's formula, boundary value problems, stability and control of random evolutions, stochastic evolutionary equations, and driven martingale measures. In addition, it treats statistics of random evolutions processes, statistics of financial stochastic models, and stochastic stability and control of financial markets.
Audience: This volume will be of interest to research and applied mathematicians working in the fields of applied probability, stochastic processes, and random evolutions, as well as experts in statistics, finance and insurance.

Risk Theory:The Stochastic Basis of Insurance (Environmental Resource Management Series)

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Risk Theory:The Stochastic Basis of Insurance (Environmental Resource Management Series)
R. Beard
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 041225980X

Stochastic Processes for Insurance and Finance.(Review): An article from: Journal of Risk and Insurance

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Stochastic Processes for Insurance and Finance.(Review): An article from: Journal of Risk and Insurance
Larry Tzeng
Manufacturer: American Risk and Insurance Association, Inc.
ProductGroup: Book
Binding: Digital

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Book Description

This digital document is an article from Journal of Risk and Insurance, published by American Risk and Insurance Association, Inc. on March 1, 2001. The length of the article is 553 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: Stochastic Processes for Insurance and Finance.(Review)
Author: Larry Tzeng
Publication: Journal of Risk and Insurance (Refereed)
Date: March 1, 2001
Publisher: American Risk and Insurance Association, Inc.
Volume: 68 Issue: 1 Page: 212

Article Type: Book Review

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SURPLUS MANAGEMENT UNDER A STOCHASTIC PROCESS.: An article from: Journal of Risk and Insurance

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SURPLUS MANAGEMENT UNDER A STOCHASTIC PROCESS.: An article from: Journal of Risk and Insurance
Larry Y. Tzeng , Jennifer L. Wang , and June H. Soo
Manufacturer: American Risk and Insurance Association, Inc.
ProductGroup: Book
Binding: Digital

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Book Description

This digital document is an article from Journal of Risk and Insurance, published by American Risk and Insurance Association, Inc. on September 1, 2000. The length of the article is 5024 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: SURPLUS MANAGEMENT UNDER A STOCHASTIC PROCESS.
Author: Larry Y. Tzeng
Publication: Journal of Risk and Insurance (Refereed)
Date: September 1, 2000
Publisher: American Risk and Insurance Association, Inc.
Volume: 67 Issue: 3 Page: 451

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