Transient and Stationary Analyses of the Surplus in a Risk Model

- Journal title : Communications for Statistical Applications and Methods
- Volume 20, Issue 6, 2013, pp.475-480
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CSAM.2013.20.6.475

Title & Authors

Transient and Stationary Analyses of the Surplus in a Risk Model

Cho, Eon Young; Choi, Seung Kyoung; Lee, Eui Yong;

Cho, Eon Young; Choi, Seung Kyoung; Lee, Eui Yong;

Abstract

The surplus process in a risk model is stochastically analyzed. We obtain the characteristic function of the level of the surplus at a finite time, by establishing and solving an integro-differential equation for the distribution function of the surplus. The characteristic function of the stationary distribution of the surplus is also obtained by assuming that an investment of the surplus is made to other business when the surplus reaches a sufficient level. As a consequence, we obtain the first and second moments of the surplus both at a finite time and in an infinite horizon (in the long-run).

Keywords

Risk model;surplus process;characteristic function;integro-differential equation;stationary distribution;

Language

English

Cited by

1.

Stationary distribution of the surplus process in a risk model with a continuous type investment,;;;

2.

Stationary analysis of the surplus process in a risk model with investments,;

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