2020/12/17 by Alexander Glauner, Glauner, Alexander
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #90C40 (Secondary) #91G05 (Primary) 91G70 #FOS: Economics and business #FOS: Mathematics #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Risk Management (q-fin.RM) #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2012.09648
openalex publication_date 2020/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the classical static optimal reinsurance problem, the cost of capital for\nthe insurer's risk exposure determined by a monetary risk measure is minimized\nover the class of reinsurance treaties represented by increasing Lipschitz\nretained loss functions. In this paper, we consider a dynamic extension of this\nreinsurance problem in discrete time which can be viewed as a risk-sensitive\nMarkov Decision Process. The model allows for both insurance claims and premium\nincome to be stochastic and operates with general risk measures and premium\nprinciples. We derive the Bellman equation and show the existence of a\nMarkovian optimal reinsurance policy. Under an infinite planning horizon, the\nmodel is shown to be contractive and the optimal reinsurance policy to be\nstationary. The results are illustrated with examples where the optimal policy\ncan be determined explicitly.\n