Journal of Applied Probability

The finite-time ruin probability with dependent insurance and financial risks

Yiqing Chen

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Abstract

Consider a discrete-time insurance risk model. Within period i, the net insurance loss is denoted by a real-valued random variable Xi. The insurer makes both risk-free and risky investments, leading to an overall stochastic discount factor Yi from time i to time i - 1. Assume that (Xi, Yi), iN, 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.

Article information

Source
J. Appl. Probab. Volume 48, Number 4 (2011), 1035-1048.

Dates
First available in Project Euclid: 16 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1324046017

Digital Object Identifier
doi:10.1239/jap/1324046017

Mathematical Reviews number (MathSciNet)
MR2896666

Zentralblatt MATH identifier
1230.91069

Subjects
Primary: 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 62E10: Characterization and structure theory 91B30: Risk theory, insurance

Keywords
Asymptotics Farlie-Gumbel-Morgenstern distribution maximum domain of attraction finite-time ruin probability subexponential distribution

Citation

Chen, Yiqing. The finite-time ruin probability with dependent insurance and financial risks. J. Appl. Probab. 48 (2011), no. 4, 1035--1048. doi:10.1239/jap/1324046017. https://projecteuclid.org/euclid.jap/1324046017.


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