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Ruin probabilities of small noise jump‐diffusions with heavy tails

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  • Ilya Pavlyukevich

Abstract

Let Xε(x) be a solution of a stochastic differential equation ${\rm d} X^{\varepsilon}_{t} = f{(X_{t}^{\varepsilon})}{\rm d}t+\varepsilon {\rm d}L_t, \, X_{0}^{\varepsilon} (x) = x > 0, \, t\epsilon {[0,1]}$, where L is a Lévy process with heavy tails. In the limit of the scale parameter ε ↓ 0 we determine the finite horizon ruin probability P$({\rm inf}_{t\epsilon{[0,1]}} X_{t}^{\varepsilon} (x)

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  • Ilya Pavlyukevich, 2008. "Ruin probabilities of small noise jump‐diffusions with heavy tails," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(1), pages 65-82, January.
    • Handle: RePEc:wly:apsmbi:v:24:y:2008:i:1:p:65-82
    DOI: 10.1002/asmb.696
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    Cited by:

    1. Henrik Hult & Filip Lindskog, 2011. "Ruin probabilities under general investments and heavy-tailed claims," Finance and Stochastics, Springer, vol. 15(2), pages 243-265, June.
    2. Yasutaka Shimizu, 2017. "Threshold Estimation for Stochastic Processes with Small Noise," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 951-988, December.

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