The perturbed compound Poisson risk model with two-sided jumps.

*(English)*Zbl 1185.91198In this rather technical paper, the authors study a classical compound Poisson risk model perturbed by a Brownian motion with two-sided jumps. The upward jumps can be interpreted as the random gains of an insurance company, the downward jumps being the random losses. Defective renewal equations, discounted penalty functions (at ruin caused by a jump or caused by oscillation) and their Laplace transforms are derived. Asymptotic behavior for the probability of ruin is studied in the case the loss jumps are heavy-tailed. A numerical example concludes the paper.

Reviewer: Giovanni Puccetti (Firenze)

##### MSC:

91G80 | Financial applications of other theories |

91B30 | Risk theory, insurance (MSC2010) |

##### Keywords:

compound Poisson risk model; discounted penalty function; Laplace transform; defective renewal equation; asymptotic formula
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\textit{Z. Zhang} et al., J. Comput. Appl. Math. 233, No. 8, 1773--1784 (2010; Zbl 1185.91198)

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