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.
Highlights
The dividend problem has long been an important issue in finance and actuarial sciences
We investigate 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 {Jn}n≥0
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
Summary
The dividend problem has long been an important issue in finance and actuarial sciences. For more recent studies about dividend problems, see [1]-[4] In these papers, they extend the threshold dividend strategy to the multiple case, and make in-depth study of the model by the probabilistic and differential equation approaches. (2016) Markov-Dependent Risk Model with Multi-Layer Dividend Strategy and Investment Interest under Absolute Ruin. To the best of our knowledge, Markov-dependent risk model with multi-layer dividend strategy and investment interest under absolute ruin has not been investigated.
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