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

2016/05/15 by Ewa Marciniak, Marciniak, Ewa, Zbigniew Palmowski +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #FOS: Economics and business #FOS: Mathematics #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Pricing of Securities (q-fin.PR) #Probability and Risk Models #math.OC #q-fin.PR

paper · pdf · doi:10.48550/arxiv.1605.04584

arxiv created 2016/05/15 · openalex publication_date 2016/05/15 · arxiv updated 2016/05/17 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

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, while claims refer to profits. We calculate the mean of the cumulative discounted dividends paid until ruin, if the barrier strategy is applied. We formulate associated Hamilton-Jacobi-Bellman equation and identify sufficient conditions for a barrier strategy to be optimal. Some numerical examples are provided when profits have exponential law.

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