Asymptotic analysis of risk quantities conditional on ruin for multidimensional heavy-tailed random walks |
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| Affiliation: | 1. Department of Statistics, Columbia University, 1255 Amsterdam Avenue, New York, NY, 10027, USA;2. Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong;1. Lamsin-Enit, Tunis El Manar University, Tunisia;2. Lamsin-Enit, Tunis El Manar University, Insat, Carthage University, Tunisia;1. Sobolev Institute of Mathematics, Ac. Koptyug avenue 4, 630090 Novosibirsk, Russia;2. School of Mathematics and Statistics, The University of Melbourne, Parkville 3010, Australia |
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| Abstract: | In this paper we consider a multidimensional renewal risk model with regularly varying claims. This model may be used to describe the surplus of an insurance company possessing several lines of business where a large claim possibly puts multiple lines in a risky condition. Conditional on the occurrence of ruin, we develop asymptotic approximations for the average accumulated number of claims leading the process to a rare set, and the expected total amount of shortfalls to this set in finite and infinite horizons. Furthermore, for the continuous time case, asymptotic results regarding the total occupation time of the process in a rare set and time-integrated amount of shortfalls to a rare set are obtained. |
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| Keywords: | Multivariate regularly variation Heavy-tailed increments Hitting rare set Lyapunov inequality |
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