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Optimal proportional reinsurance policies for diffusion models

Authors:	B Højgaard M Taksar

Institution:	1. Department of Mathematics , Aalborg University , Fr. Bajersvej 7E, DK-9220 , Aalborg , Denmark E-mail: malik@math.auc.dk;2. Department of AMS , SUNY-Stony Brook , Stony Brook , NY , 11794-3600 , USA E-mail: taksar@ams.sunysb.edu

Abstract:	Abstract When applying a proportional reinsurance policy π the reserve of the insurance company $/></span>=(<i>a<sub>π</sub> </i>(<i>t</i>)<i>u</i> <i>dt</i> + <i>a<sub>π</sub> </i>(<i>t</i>)<i>σ dW<sub>t</sub> </i> where {<i>W<sub>t</sub> </i>} is a standard Brownian motion, <i>µ, π</i>, > 0 are constants and 0 ? <i>a<sub>π</sub> </i>(<i>t</i>) ? 1 is the control process, where <i>a<sub>π</sub> </i>(<i>t</i>) denotes the fraction, that is reinsured at time <i>t</i>. The aim of this paper is to find a policy that maximizes the return function <i>V<sub>π</sub> </i>(<i>x</i>) = <span class=$
Keywords:	Diffusion models stochastic control HJB equation