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A ruin problem for classical risk processes under random interest force. (Chinese) Zbl 1083.62106
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 H. U. Gerber and 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 α.
MSC:
62P05Applications of statistics to actuarial sciences and financial mathematics
91B30Risk theory, insurance
60J70Applications of Brownian motions and diffusion theory
60G35Signal detection and filtering (stochastic processes)