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Risk analysis in finance and insurance

Author: A V Melʹnikov
Publisher: Boca Raton, Fla. : CRC ; London : Taylor & Francis [distributor], ©2011.
Series: Chapman & Hall/CRC monographs and surveys in pure and applied mathematics, 131
Edition/Format:   Book : English : 2nd edView all editions and formats

The development of quantitative methods based on stochastic analysis is a key achievement of modern financial mathematics. This book presents an introduction to the main ideas, methods, and  Read more...

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Document Type: Book
All Authors / Contributors: A V Melʹnikov
ISBN: 9781420070521 1420070525
Language Note: Translated into English.
OCLC Number: 540161446
Notes: Previous edition: 2004.
Description: x, 318 pages ; 24 cm.
Contents: Financial Risk Management and Related Mathematical Tools Introductory concepts of the securities market Probabilistic foundations of financial modelling and pricing of contingent claims Elements of probability theory and stochastic analysis Financial Risk Management in the Binomial Model The binomial model of a financial market. Absence of arbitrage, uniqueness of a risk-neutral probability measure, martingale representation Hedging contingent claims in the binomial market model. The Cox-Ross-Rubinstein formula Pricing and hedging American options Utility functions and St. Petersburg's paradox. The problem of optimal investment The term structure of prices, hedging and investment strategies in the Ho-Lee model The transition from the binomial model of a financial market to a continuous model. The Black-Scholes formula and equation Advanced Analysis of Financial Risks: Discrete Time Models Fundamental theorems on arbitrage and completeness. Pricing and hedging contingent claims in complete and incomplete markets The structure of options prices in incomplete markets and in markets with constraints Hedging contingent claims in mean square Gaussian model of a financial market in discrete time. Insurance appreciation and discrete version of the Black-Scholes formula Analysis of Risks: Continuous Time Models The Black-Scholes model. "Greek" parameters in risk management, hedging and optimal investment Beyond the Black-Scholes model Imperfect hedging and risk measures Fixed Income Securities: Modeling and Pricing Elements of deterministic theory of fixed income instruments Stochastic modelling and pricing bonds and their derivatives Implementations of Risk Analysis in Various Areas of Financial Industry Real options: pricing long-term investment projects Technical analysis in risk management Performance measures and their applications Insurance and Reinsurance Risks Modelling risk in insurance and methodologies of premium calculations Risks transfers via reinsurance Elements of traditional life insurance Risk modelling and pricing in innovative life insurance Solvency Problem for an Insurance Company Ruin probability as a measure of solvency of an insurance company Solvency of an insurance company and investment portfolios Solvency problem in a generalized Cramer-Lundberg model Appendix A: Problems Appendix B: Bibliographic Remarks Bibliography Glossary of Notation Index
Series Title: Chapman & Hall/CRC monographs and surveys in pure and applied mathematics, 131
Responsibility: Alexander Melʹnikov.
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"... a well-chosen collection of topics from risk analysis and management for finance and actuarial science illustrated with solved problems." -Christel Geiss, Mathematical Reviews, November 2013 Read more...

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