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Exponential Asymptotical Expansions for Ruin Probability in a Classical Risk Process with Non-polynomial Perturbations

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Modern Problems in Insurance Mathematics

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Abstract

In this chapter we investigate the asymptotical behaviour of ruin probability in a classical compound Poisson risk process associated with perturbations in the claim size distributions and/or other parameters of the risk process. The novelty of this study is that we consider non-polynomial perturbations which include the standard polynomial perturbations as particular cases. The aim of the study is to develop exponential asymptotical expansions for the ruin probability as the initial capital goes to infinity and the perturbation parameter goes to zero, simultaneously but in a balanced manner. Numerical examples of risk processes with such type of perturbations are also given for illustrative purposes.

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Authors and Affiliations

  1. Mälardalen University, Västerås, Sweden

    Ying Ni

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  1. Ying Ni
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Correspondence to Ying Ni .

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Editors and Affiliations

  1. Department of Mathematics Professor of Mathematical Statistics, Stockholm University, Stockholm, Sweden

    Dmitrii Silvestrov

  2. Department of Mathematics Professor in Mathematical Statistics, Stockholm University, Stockholm, Sweden

    Anders Martin-Löf

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Ni, Y. (2014). Exponential Asymptotical Expansions for Ruin Probability in a Classical Risk Process with Non-polynomial Perturbations. In: Silvestrov, D., Martin-Löf, A. (eds) Modern Problems in Insurance Mathematics. EAA Series. Springer, Cham. https://doi.org/10.1007/978-3-319-06653-0_6

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