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Ruin probabilities [electronic resource] / S�ren Asmussen, Hansj�org Albrecher.

By: Asmussen, S�ren.
Contributor(s): Albrecher, Hansj�org.
Material type: TextTextSeries: Advanced series on statistical science & applied probability: v. 14.Publisher: Singapore ; Hackensack, NJ : World Scientific, c2010Edition: 2nd ed.Description: 1 online resource (xvii, 602 p.) : ill.ISBN: 9789814282536 (electronic bk.); 9814282537 (electronic bk.).Subject(s): Insurance -- Mathematics | Risk | Risk (Insurance) -- Mathematical models | Social Science | Business | BUSINESS & ECONOMICS -- Insurance -- Risk Assessment & ManagementGenre/Form: Electronic books.Additional physical formats: Print version:: Ruin probabilities.DDC classification: 368/.01 Online resources: EBSCOhost
Contents:
Introduction -- Martingales and simple ruin calculations -- Further general tools and results -- The compound Poisson model -- The probability of ruin within finite time -- Renewal arrivals -- Risk theory in a Markovian environment -- Level-dependent risk processes -- Matrix-analytic methods -- Ruin probabilities in the presence of heavy tails -- Ruin probabilities for L�evy processes -- Gerber-Shiu functions -- Further models with dependency -- Stochastic control -- Simulation methodology -- Miscellaneous topics.
Summary: The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramer-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber-Shiu functions and dependence.
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Includes bibliographical references and index.

Introduction -- Martingales and simple ruin calculations -- Further general tools and results -- The compound Poisson model -- The probability of ruin within finite time -- Renewal arrivals -- Risk theory in a Markovian environment -- Level-dependent risk processes -- Matrix-analytic methods -- Ruin probabilities in the presence of heavy tails -- Ruin probabilities for L�evy processes -- Gerber-Shiu functions -- Further models with dependency -- Stochastic control -- Simulation methodology -- Miscellaneous topics.

The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramer-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber-Shiu functions and dependence.

Description based on print version record.

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Ruin probabilities by Asmussen, S�ren. ©2010
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