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The Finite-Time Ruin Probability with Dependent Insurance and Financial Risks

Part of: Applications Distribution theory Mathematical economics

Published online by Cambridge University Press:  14 July 2016

Yiqing Chen
Yiqing Chen*
Affiliation:
University of Liverpool
*
∗ Postal address: Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, UK. Email address: yiqing.chen@liv.ac.uk
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Abstract

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Consider a discrete-time insurance risk model. Within period i, the net insurance loss is denoted by a real-valued random variable X i . The insurer makes both risk-free and risky investments, leading to an overall stochastic discount factor Y i from time i to time i − 1. Assume that (X i , Y i ), i ∈ N, form a sequence of independent and identically distributed random pairs following a common bivariate Farlie-Gumbel-Morgenstern distribution with marginal distribution functions F and G. When F is subexponential and G fulfills some constraints in order for the product convolution of F and G to be subexponential too, we derive a general asymptotic formula for the finite-time ruin probability. Then, for special cases in which F belongs to the Fréchet or Weibull maximum domain of attraction, we improve this general formula to be transparent.

Keywords

AsymptoticsFarlie-Gumbel-Morgenstern distributionmaximum domain of attractionfinite-time ruin probabilitysubexponential distribution

MSC classification

Secondary: 62P05: Applications to actuarial sciences and financial mathematics 62E10: Characterization and structure theory 91B30: Risk theory, insurance
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 4 , December 2011 , pp. 1035 - 1048
Copyright
Copyright © Applied Probability Trust 2011 

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