Optimal dynamic reinsurance policies for large insurance portfolios
type: Item
instance of: scholarly article
title: Optimal dynamic reinsurance policies for large insurance portfolios
zbMATH Open document ID: 1066.91052
author: Charlotte Markussen
author: Michael Taksar
published in: Finance and Stochastics
publication date: 2004-03-16T00:00:00Z
review text: The authors consider a problem of minimization of the ruin probability for an insurance company whose surplus is relatively large compared to the size of individual claim and is modelled by a diffusion process. It is assumed that without reinsurance the dynamics of the insurance company surplus is described by the equation \[ dR_t=\mu dt+\sigma dw^{(1)}_t,\quad R_0=x, \] and for the proportional reinsurance the corresponding diffusion approximation becomes \[ dR_t=(\mu-(1-a)\lambda)dt+\sigma dw^{(1)}_t, \] where \(0\leq a\leq 1\) is called risk exposure, \(\lambda\geq \mu\). In addition, it is assumed that all of the surplus is invested in a stock market instrument, whose price is governed by the classical Black-Scholes dynamics \[ dP_t =rP_tdt+\sigma_pP_tdw^{(2)}_t. \] Stochastic optimal control theory is used to determine the optimal reinsurance policy which minimizes the ruin probability of the cedent. It is demonstrated that the optimal policy of the cedent depend significantly on the nature of the investment available, in particular on its volatility. The economic analysis of all possible relations between coefficients is given and numerical results are presented.
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 60H30
zbMATH DE Number: 2059101
zbMATH Keywords: stochastic control
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: Black-Scholes model
zbMATH Keywords: controlled stochastic processes
zbMATH Keywords: proportional reinsurance
zbMATH Keywords: investments
zbMATH Keywords: ruin probabilities
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: s007800200073
OpenAlex ID: W2082046266
DOI: 10.1007/S007800200073
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description: scientific article; zbMATH DE number 2059101