On modifications of ruin processes. (English. Ukrainian original) Zbl 0923.60049

Gusak, D. V.

Theory Probab. Math. Stat. 56, 87-95 (1998); translation from Teor. Jmovirn. Mat. Stat. 56, 87-95 (1997).

The classical risk processes (c.r.p.) in the insurance mathematics are defined by homogeneous Poisson processes with positive drift and negative jumps. The main problem for c.r.p. is to find the ruin probability on finite and infinite intervals. The author gives modifications of c.r.p. connected with an instant reflection from barrier \(B>0\) and with reflection after exponentially distributed delaying on \(B>0.\) Under some conditions the ergodic distribution for the modified c.r.p. and relations for the ruin probability are proved. Relations for integral transformations of distribution of both modified risk processes are obtained.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60G50	Sums of independent random variables; random walks
60K10	Applications of renewal theory (reliability, demand theory, etc.)
60K15	Markov renewal processes, semi-Markov processes
60J70	Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
62P05	Applications of statistics to actuarial sciences and financial mathematics

Keywords:

risk process; ruin probability; ergodic distribution