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	An insurance risk model with stochastic volatility
	Chi, Yichun ; Jaimungal, Sebastian ; Lin, X. Sheldon
	2010
关键词	Gerber-Shiu expected discounted penalty function Integro-differential equation Singular perturbation theory Stochastic volatility Perturbed compound Poisson risk process Phase-type distribution Ornstein-Uhlenbeck process EXPECTED DISCOUNTED PENALTY DEFECTIVE RENEWAL EQUATION JUMP-DIFFUSION RUIN MOMENTS TIME APPROXIMATIONS SURPLUS OPTIONS DEFICIT
英文摘要	In this paper, we extend the Cramer-Lundberg insurance risk model perturbed by diffusion to incorporate stochastic volatility and Study the resulting Gerber-Shiu expected discounted penalty (EDP) function. Under the assumption that volatility is driven by an underlying Ornstein-Uhlenbeck (OU) process, we derive the integro-differential equation which the EDP function satisfies. Not surprisingly, no closed-form solution exists: however, assuming the driving OU process is fast mean-reverting, we apply the singular perturbation theory to obtain an asymptotic expansion of the Solution. Two integro-differential equations for the first two terms in this expansion are obtained and explicitly solved. When the claim size distribution is of phase-type, the asymptotic results simplify even further and we succeed in estimating the error of the approximation. Hyper-exponential and mixed-Erlang distributed claims are considered in some detail. (C) 2009 Elsevier B.V. All rights reserved.; Economics; Mathematics, Interdisciplinary Applications; Social Sciences, Mathematical Methods; Statistics & Probability; SCI(E); SSCI; 1; ARTICLE; 1,SI; 52-66; 46
语种	英语
出处	SCI
出版者	insurance mathematics economics
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/245466]
专题	数学科学学院
推荐引用方式 GB/T 7714	Chi, Yichun,Jaimungal, Sebastian,Lin, X. Sheldon. An insurance risk model with stochastic volatility. 2010-01-01.

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