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Optimal Risk Control for The Excess of Loss Reinsurance Policies

Published online by Cambridge University Press:  09 August 2013

Hui Meng  and
Xin Zhang
Xin Zhang
Affiliation:
School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P.R. China
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Abstract

The primary objective of the paper is to explore using reinsurance as a risk management tool for an insurance company. We consider an insurance company whose surplus can be modeled by a Brownian motion with drift and that the surplus can be invested in a risky or riskless asset. Under the above Black-Scholes type framework and using the objective of minimizing the ruin probability of the insurer, we formally establish that the excess-of-loss reinsurance treaty is optimal among the class of plausible reinsurance treaties. We also obtain the optimal level of retention as well as provide an explicit expression of the minimal probability of ruin.

Keywords

Excess of lossMinimal probability of ruinStochastic controlInvestmentsHamilton-Jacobi-Bellman equation
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 179 - 197
Copyright
Copyright © International Actuarial Association 2010

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