Optimal combinational quota‐share and excess‐of‐loss reinsurance policies in a dynamic setting

In this paper, we describe a large insurance company's surplus by a Brownian motion with positive drift, which is the approximation of a classical risk process. The problem of minimizing the probability of ruin by controlling the combinational quota‐share and excess‐of‐loss reinsurance strategy is considered. We show that the optimal combinational reinsurance strategy must be the pure excess‐of‐loss reinsurance strategy. Moreover, we give an explicit solution for the optimal reinsurance strategy. Copyright © 2006 John Wiley & Sons, Ltd.

[1]  J. Paulsen,et al.  Optimal control of risk exposure, reinsurance and investments for insurance portfolios , 2004 .

[2]  Søren Asmussen,et al.  Controlled diffusion models for optimal dividend pay-out , 1997 .

[3]  A. Shiryaev,et al.  Optimization of the flow of dividends , 1995 .

[4]  L. Centeno.  On Combining Quota-Share and Excess of Loss , 1985, ASTIN Bulletin.

[5]  Bjarne Højgaard,et al.  Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy , 2004 .

[6]  An insight into the excess of loss retention limit , 1991 .

[7]  Michael I. Taksar,et al.  Optimal risk and dividend distribution control models for an insurance company , 2000, Math. Methods Oper. Res..

[8]  H. Gjessing,et al.  Properties of functions of the excess of loss retention limit with applications , 1994 .

[9]  M. Milevsky.  Real Longevity Insurance with a Deductible: Introduction to Advanced-Life Delayed Annuities (ALDA) , 2005 .

[10]  J. Grandell.  Aspects of Risk Theory , 1991 .

[11]  Sid Browne,et al.  Optimal Investment Policies for a Firm With a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin , 1995, Math. Oper. Res..

[12]  M. D. L. Centeno.  Excess of loss reinsurance and Gerber's inequality in the Sparre Anderson model , 2002 .

[13]  H. Schmidli,et al.  On minimizing the ruin probability by investment and reinsurance , 2002 .

[14]  Xun Yu Zhou,et al.  A Diffusion Model for Optimal Dividend Distribution for a Company with Constraints on Risk Control , 2002, SIAM J. Control. Optim..

[15]  M. D. L. Centeno.  Dependent risks and excess of loss reinsurance , 2005 .

[16]  Søren Asmussen,et al.  Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation , 2000, Finance Stochastics.

[17]  Excess of loss reinsurance limits , 1979 .

[18]  Michael Vogt,et al.  Optimal Dynamic XL Reinsurance , 2001, ASTIN Bulletin.

[19]  Hanspeter Schmidli,et al.  Optimal Proportional Reinsurance Policies in a Dynamic Setting , 2001 .