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Finite- and Infinite-Time Ruin Probabilities with General Stochastic Investment Return Processes and Bivariate Upper Tail Independent and Heavy-Tailed Claims

Part of: Mathematical economics Applications

Published online by Cambridge University Press:  04 January 2016

Fenglong Guo  and
Dingcheng Wang
Fenglong Guo
Affiliation:
Nanjing Audit University, and University of Electronic Science and Technology of China
Dingcheng Wang*
Affiliation:
Nanjing Audit University, Australian National University, and University of Electronic Science and Technology of China
*
∗ Postal address: Center of Financial Engineering, Nanjing Audit University, Nanjing 211815, China. Email address: [email protected]
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Abstract

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In this paper we investigate the asymptotic behaviors of the finite- and infinite-time ruin probabilities for a Poisson risk model with stochastic investment returns which constitute a general adapted càdlàg process and heavy-tailed claim sizes which are bivariate upper tail independent. The results of this paper show that the asymptotic ruin probabilities are dominated by the extreme of insurance risk but not by that of investment risk. As applications of the results, we discuss four special cases when the investment returns are determined by a fractional Brownian motion, an integrated Vasicek model, an integrated Cox–Ingersoll–Ross model, and the Heston model.

Keywords

ruin probabilityheavy tailinvestment return processupper tail dependencefractional Brownian motionVasicek modelCox–Ingersoll–Ross modelHeston model

MSC classification

Primary: 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 62P20: Applications to economics 91B30: Risk theory, insurance
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 45 , Issue 1 , March 2013 , pp. 241 - 273
Copyright
© Applied Probability Trust 

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