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Zbl 1083.62106
Zhao, Xia; Liu, Jin-e
A ruin problem for classical risk processes under random interest force.
(Chinese. English summary)
[J] Appl. Math., Ser. A (Chin. Ed.) 20, No. 3, 313-319 (2005). ISSN 1000-4424

Summary: The interest force accumulated process is modeled by a standard Brownian motion and a Poisson process. By a martingale approach, Lundberg's fundamental equation is obtained and two efficient applications of its solutions are considered. Hence some results about the probability of ruin and the probability that the surplus reaches a given level $x$ $(x> u)$ are obtained. The results are a generalization of {\it H. U. Gerber} and {\it E. S. W. Shiu} [Insur. Math. Econ. 24, 3--14 (1999; Zbl 0939.91065)] under constant interest force. Finally, some results are obtained when the individual claim amount obeys the exponential distribution with parameter $\alpha$.
MSC 2000:
*62P05 Appl. of statistics to actuarial sciences and financial mathematics
91B30 Risk theory etc.
60J70 Appl. of diffusion theory
60G35 Appl. of stochastic processes

Keywords: ruin probability

Citations: Zbl 0939.91065

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