On the Optimal Dividend Problem for Insurance Risk Models with Surplus-Dependent Premiums

Ewa Marciniak and Zbigniew Palmowski ()
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Ewa Marciniak: AGH University of Science and Technology
Zbigniew Palmowski: University of Wrocław

Journal of Optimization Theory and Applications, 2016, vol. 168, issue 2, No 19, 723-742

Abstract: Abstract This paper concerns an optimal dividend distribution problem for an insurance company with surplus-dependent premium. In the absence of dividend payments, such a risk process is a particular case of so-called piecewise deterministic Markov processes. The control mechanism chooses the size of dividend payments. The objective consists in maximizing the sum of the expected cumulative discounted dividend payments received until the time of ruin and a penalty payment at the time of ruin, which is an increasing function of the size of the shortfall at ruin. A complete solution is presented to the corresponding stochastic control problem. We identify the associated Hamilton–Jacobi–Bellman equation and find necessary and sufficient conditions for optimality of a single dividend-band strategy, in terms of particular Gerber–Shiu functions. A number of concrete examples are analyzed.

Keywords: Optimal strategy; PDMP; Barrier strategy; Integro-differential HJB equation; Gerber–Shiu function; Stochastic controls; 60G51; 60G50; 60K25; 93E20 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-015-0755-3

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