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Finite- and infinite-time ruin probabilities in the presence of stochastic returns on investments

Part of: Distribution theory Applications Mathematical economics

Published online by Cambridge University Press:  01 July 2016

Qihe Tang  and
Gurami Tsitsiashvili
Qihe Tang*
Affiliation:
Concordia University
Gurami Tsitsiashvili*
Affiliation:
Russian Academy of Sciences
*
∗ Postal address: Department of Mathematics and Statistics, Concordia University, 7141 Sherbrooke Street West, Montreal, Quebec, H4B 1R6, Canada. Email address: qtang@mathstat.concordia.ca
∗∗ Current address: Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Radio str. 7, 690068 Vladivostok, Russia. Email address: guram@iam.dvo.ru
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Abstract

This paper investigates the finite- and infinite-time ruin probabilities in a discrete-time stochastic economic environment. Under the assumption that the insurance risk - the total net loss within one time period - is extended-regularly-varying or rapidly-varying tailed, various precise estimates for the ruin probabilities are derived. In particular, some estimates obtained are uniform with respect to the time horizon, and so apply in the case of infinite-time ruin.

Keywords

Asymptoticsclass S(γ)endpointextended regular variationfinancial riskinsurance riskrapid variationruin probability

MSC classification

Primary: 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 62E10: Characterization and structure theory 91B30: Risk theory, insurance
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 36 , Issue 4 , December 2004 , pp. 1278 - 1299
Copyright
Copyright © Applied Probability Trust 2004 

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