Markov-Dependent Risk Model with Multi-Layer Dividend Strategy and Investment Interest under Absolute Ruin

Abstract

In this paper, we consider the Markov-dependent risk model with multi-layer dividend strategy and investment interest under absolute ruin, in which the claim occurrence and the claim amount are regulated by an external discrete time Markov chain. We derive systems of integro-differential equations satisfied by the moment-generating function, the nth moment of the discounted dividend payments prior to absolute ruin and the Gerber-Shiu function. Finally, the matrix form of systems of integro-differential equations satisfied by the Gerber-Shiu function is presented.

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

“…Results related to perturbed compound Poisson risk models under multi-layer dividend strategies can be found in [31,42]. In addition, different classes of more general renewal risk models are investigated in [15,19,40,41], and some recent papers deal with risk models that incorporate various dependence structures (see, e.g., [21,38,46,48]).…”

The Gerber-Shiu discounted penalty function: A review from practical perspectives

“…Finally, an algebraic operator approach is developed to solve the boundary value problem leading to an analytic expression for the Gerber-Shiu function on a Sparre-Andersen model [5], and has been extended to tackle the integro-differential equation with variablecoefficients for a Sparre-Andersen model with a surplus dependent premium rate when both claim and interclaim time distributions have rational Laplace transforms [4]. Yet other boundary value problems can be found in [190] for an Erlang(n) risk model with two-sided jumps and a constant dividend barrier and in [99] for a MAP risk model with a multi-layer dividend strategy and constant interest and debit rates.…”