Rough descriptions of ruin for a general class of surplus processes. (English) Zbl 0932.60046

Nyrhinen, Harri

Adv. Appl. Probab. 30, No. 4, 1008-1026 (1998).

Let \(\{Y_n, n\geq 1\}\) be a stochastic process and \(M\) a positive real number. One can interpret \(-Y_n\) as the accumulated surplus and \(M\) as the initial capital of an insurance company. Define the time of ruin by \(T= \inf\{n: Y_n>M\}\) (\(T=+\infty\) if \(Y_n\leq M\) for \(n=1,2,\dots\)). Using the techniques of large deviations theory the author obtains rough exponential estimates for ruin probabilities for a general class of processes. He also generalizes the concept of the safety loading and considers its importance to ruin probabilities.

Reviewer: Zdzislaw Rychlik (Lublin)

MSC:

60G40	Stopping times; optimal stopping problems; gambling theory
60F10	Large deviations

Keywords:

large deviations theory; ruin problem