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On the Optimal Dividend Problem in the Dual Model with Surplus-Dependent Premiums

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

Journal of Optimization Theory and Applications, 2018, vol. 179, issue 2, No 7, 533-552

Abstract: Abstract This paper concerns the dual risk model, dual to the risk model for insurance applications, where premiums are surplus-dependent. In such a model, premiums are regarded as costs and claims refer to profits. We calculate the mean of the cumulative discounted dividends paid until the time of ruin, if the barrier strategy is applied. We formulate the associated Hamilton–Jacobi–Bellman equation and identify sufficient conditions for a barrier strategy to be optimal. Numerical examples are provided.

Keywords: Dividends; PDMP; Optimal strategy; Barrier strategy; Integro-differential HJB equation; Dual model; Stochastic control; Exit problems; 49J53; 49K99 (search for similar items in EconPapers)
Date: 2018
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