Dynamic Reinsurance in Discrete Time Minimizing the Insurer's Cost of Capital

Autor:	Glauner, Alexander
Rok vydání:	2020
Předmět:	Quantitative Finance - Risk Management Mathematics - Optimization and Control 91G05 (Primary) 91G70 90C40 (Secondary)
Druh dokumentu:	Working Paper
Popis:	In the classical static optimal reinsurance problem, the cost of capital for the insurer's risk exposure determined by a monetary risk measure is minimized over the class of reinsurance treaties represented by increasing Lipschitz retained loss functions. In this paper, we consider a dynamic extension of this reinsurance problem in discrete time which can be viewed as a risk-sensitive Markov Decision Process. The model allows for both insurance claims and premium income to be stochastic and operates with general risk measures and premium principles. We derive the Bellman equation and show the existence of a Markovian optimal reinsurance policy. Under an infinite planning horizon, the model is shown to be contractive and the optimal reinsurance policy to be stationary. The results are illustrated with examples where the optimal policy can be determined explicitly. Comment: arXiv admin note: text overlap with arXiv:2010.07220
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2012.09648 Zobrazit plný text záznamu View this record from Arxiv