Author: Søren AsmussenPublisher:
ISBN:
Category :
Languages : en
Pages : 16
Book Description
Ruin Probabilities Via Local Adjustment Coefficients
Author: Søren AsmussenRuin Probabilities
Author: S?ren AsmussenPublisher: World Scientific
ISBN: 9814282529
Category : Mathematics
Languages : en
Pages : 621
Book Description
The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramr?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.
Ruin Probabilities
Author: S?ren AsmussenPublisher: World Scientific
ISBN: 9812779310
Category : Mathematics
Languages : en
Pages : 399
Book Description
The text is a treatment of classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramer-Lundberg approximation, exact solutions, other approximations (for example, 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 or periodicity. Special features of the book are the emphasis on change of measure techniques, phase-type distributions as computational vehicle and the connection to other applied probability areas like queueing theory.
Ruin Probabilities
Author: Soren AsmussenPublisher: World Scientific
ISBN: 9814500321
Category : Mathematics
Languages : en
Pages : 399
Book Description
The book is a comprehensive treatment of classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (eg. 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 or periodicity. Special features of the book are the emphasis on change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas like queueing theory.
Stochastic Simulation: Algorithms and Analysis
Author: Søren AsmussenPublisher: Springer Science & Business Media
ISBN: 0387690336
Category : Mathematics
Languages : en
Pages : 490
Book Description
Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage. The first half of the book focuses on general methods; the second half discusses model-specific algorithms. Exercises and illustrations are included.
Applied Probability and Queues
Author: Soeren AsmussenPublisher: Springer Science & Business Media
ISBN: 0387215255
Category : Mathematics
Languages : en
Pages : 451
Book Description
"This book is a highly recommendable survey of mathematical tools and results in applied probability with special emphasis on queueing theory....The second edition at hand is a thoroughly updated and considerably expended version of the first edition.... This book and the way the various topics are balanced are a welcome addition to the literature. It is an indispensable source of information for both advanced graduate students and researchers." --MATHEMATICAL REVIEWS
Stochastic Processes for Insurance and Finance
Author: Tomasz RolskiPublisher: John Wiley & Sons
ISBN: 0470317884
Category : Mathematics
Languages : en
Pages : 680
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
Asymptotic Ruin Probabilities and Optimal Investment
Author: Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
We study the infinite time ruin probability for an insurance company in the classical Cramér-Lundberg model with finite exponential moments. The additional non-classical feature is that the company is also allowed to invest in some stock market, modeled by geometric Brownian motion. We obtain an exact analogue of the classical estimate for the ruin probability without investment, i.e., an exponential inequality. The exponent is larger than the one obtained without investment, the classical Lundberg adjustment coefficient, and thus one gets a sharper bound on the ruin probability. A surprising result is that the trading strategy yielding the optimal asymptotic decay of the ruin probability simply consists in holding a fixed quantity (which can be explicitly calculated) in the risky asset, independent of the current reserve. This result is in apparent contradiction to the common believe that 'rich' companies should invest more in risky assets than 'poor' ones. The reason for this seemingly paradoxical result is that the minimization of the ruin probability is an extremely conservative optimization criterion, especially for 'rich' companies. (author's abstract).
Characteristics of Ruin Probabilities in Classical Risk Models with and Without Investment, Cox Risk Models and Perturbed Risk Models
Author: Hanspeter SchmidliPublisher:
ISBN:
Category : Risk
Languages : en
Pages : 58
Book Description
Author: