A Generalization of the Discounted Penalty Function in Ruin Theory
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Date
2008-08-21T15:54:18Z
Authors
Feng, Runhuan
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
As ruin theory evolves in recent years, there has been a variety of quantities pertaining to an insurer's bankruptcy at the centre of focus in the literature. Despite the fact that these quantities are distinct from each other, it was brought to our attention that many solution methods apply to nearly all ruin-related quantities. Such a peculiar similarity among their solution
methods inspired us to search for a general form that reconciles
those seemingly different ruin-related quantities.
The stochastic approach proposed in the thesis addresses such issues and contributes to the current literature in three major directions.
(1) It provides a new function that unifies many existing
ruin-related quantities and that produces more new quantities of
potential use in both practice and academia.
(2) It applies generally to a vast majority of risk processes and permits the consideration of combined effects of investment strategies, policy modifications, etc, which were either impossible or difficult tasks using traditional approaches.
(3) It gives a shortcut to the derivation of intermediate solution equations. In addition to the efficiency, the new approach also leads to a standardized procedure to cope with various situations.
The thesis covers a wide range of ruin-related and financial topics while developing the unifying stochastic approach. Not only does it attempt to provide insights into the unification of quantities in ruin theory, the thesis also seeks to extend its applications in other related areas.
Description
Keywords
ruin theory, discounted penalty function, generalized Gerber-Shiu function, Piecewise-deterministic Markov process, Sparre Andersen model, Jump diffusion process, total dividends paid up to ruin, infinitesimal generator