2020/01/11 by Julia Eisenberg, Eisenberg, Julia, 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 #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Probability and Risk Models #math.PR #q-fin.MF
paper · pdf · doi:10.48550/arxiv.2001.03733
arXiv admin note: text overlap with arXiv:1604.06892
arxiv created 2020/01/11 · openalex publication_date 2020/01/11 · arxiv updated 2020/01/14 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
This paper considers an optimal dividend distribution problem for an insurance company where the dividends are paid in a foreign currency. In the absence of dividend payments, our risk process follows a spectrally negative Lévy process. We assume that the exchange rate is described by a an exponentially Lévy process, possibly containing the same risk sources like the surplus of the insurance company under consideration. The control mechanism chooses the amount of dividend payments. The objective is to maximise the expected 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. Via the corresponding Hamilton--Jacobi--Bellman equation we find the necessary and sufficient conditions for optimality of a single dividend barrier strategy. A number of numerical examples illustrate the theoretical analysis.