The risk model with stochastic premiums and a multi-layer dividend strategy

TL;DR

This paper extends classical risk models by incorporating stochastic premiums and a multi-layer dividend strategy, deriving equations for key risk measures and providing explicit formulas in specific cases, supported by numerical examples.

Contribution

It introduces a generalized risk model with stochastic premiums and multi-layer dividends, deriving new equations and explicit solutions for ruin probabilities and dividends.

Findings

Derived piecewise integro-differential equations for the Gerber--Shiu function.

Obtained explicit formulas for ruin probability and expected dividends in exponential cases.

Provided numerical illustrations demonstrating multi-layer dividend strategies.

Abstract

The paper deals with a generalization of the risk model with stochastic premiums where dividends are paid according to a multi-layer dividend strategy. First of all, we derive piecewise integro-differential equations for the Gerber--Shiu function and the expected discounted dividend payments until ruin. In addition, we concentrate on the detailed investigation of the model in the case of exponentially distributed claim and premium sizes and find explicit formulas for the ruin probability as well as for the expected discounted dividend payments. Lastly, numerical illustrations for some multi-layer dividend strategies are presented.