Open Access
August 2015 Interplay of insurance and financial risks in a discrete-time model with strongly regular variation
Jinzhu Li, Qihe Tang
Bernoulli 21(3): 1800-1823 (August 2015). DOI: 10.3150/14-BEJ625


Consider an insurance company exposed to a stochastic economic environment that contains two kinds of risk. The first kind is the insurance risk caused by traditional insurance claims, and the second kind is the financial risk resulting from investments. Its wealth process is described in a standard discrete-time model in which, during each period, the insurance risk is quantified as a real-valued random variable $X$ equal to the total amount of claims less premiums, and the financial risk as a positive random variable $Y$ equal to the reciprocal of the stochastic accumulation factor. This risk model builds an efficient platform for investigating the interplay of the two kinds of risk. We focus on the ruin probability and the tail probability of the aggregate risk amount. Assuming that every convex combination of the distributions of $X$ and $Y$ is of strongly regular variation, we derive some precise asymptotic formulas for these probabilities with both finite and infinite time horizons, all in the form of linear combinations of the tail probabilities of $X$ and $Y$. Our treatment is unified in the sense that no dominating relationship between $X$ and $Y$ is required.


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Jinzhu Li. Qihe Tang. "Interplay of insurance and financial risks in a discrete-time model with strongly regular variation." Bernoulli 21 (3) 1800 - 1823, August 2015.


Received: 1 January 2013; Revised: 1 November 2013; Published: August 2015
First available in Project Euclid: 27 May 2015

zbMATH: 1336.91048
MathSciNet: MR3352061
Digital Object Identifier: 10.3150/14-BEJ625

Keywords: (strongly) regular variation , asymptotics , convolution equivalence , financial risk , insurance risk , ruin probabilities , tail probabilities

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

Vol.21 • No. 3 • August 2015
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