Optimal dividend and reinsurance in the presence of two reinsurers

In this paper the optimal dividend (subject to transaction costs) and reinsurance (with two reinsurers) problem is studied in the limit diffusion setting. It is assumed that transaction costs and taxes are required when dividends occur, and that the premiums charged by two reinsurers are calculated according to the exponential premium principle with different parameters, which makes the stochastic control problem nonlinear. The objective of the insurer is to determine the optimal reinsurance and dividend policy so as to maximize the expected discounted dividends until ruin. The problem is formulated as a mixed classical-impulse stochastic control problem. Explicit expressions for the value function and the corresponding optimal strategy are obtained. Finally, a numerical example is presented to illustrate the impact of the parameters associated with the two reinsurers' premium principle on the optimal reinsurance strategy.

[1]  Ming Zhou,et al.  Optimal reinsurance and dividend for a diffusion model with capital injection: Variance premium principle , 2012 .

[2]  Junyi Guo,et al.  Optimal excess-of-loss reinsurance and dividend payments with both transaction costs and taxes , 2010 .

[3]  Xun Yu Zhou,et al.  Excess-of-loss reinsurance for a company with debt liability and constraints on risk reduction , 2001 .

[4]  Marek Musiela,et al.  An example of indifference prices under exponential preferences , 2004, Finance Stochastics.

[5]  M. Kaluszka.  Optimal reinsurance under mean-variance premium principles , 2001 .

[6]  Thaleia Zariphopoulou,et al.  Pricing Dynamic Insurance Risks Using the Principle of Equivalent Utility , 2002 .

[7]  Virginia R. Young,et al.  Optimal insurance under Wang’s premium principle , 1999 .

[8]  Lei Zhang,et al.  CLASSICAL AND IMPULSE STOCHASTIC CONTROL FOR THE OPTIMIZATION OF THE DIVIDEND AND RISK POLICIES OF AN INSURANCE FIRM , 2006 .

[9]  Alexandru Badescu,et al.  Optimal Risk Transfer under Quantile-Based Risk Measures , 2013 .

[10]  Tak Kuen Siu,et al.  Optimal Mixed Impulse-Equity Insurance Control Problem With Reinsurance , 2011, SIAM J. Control. Optim..

[11]  Hui Meng,et al.  Optimal Reinsurance Arrangements in the Presence of Two Reinsurers , 2012 .

[12]  X. Guoa,et al.  A constrained non-linear regular-singular stochastic control problem , with applications , 2003 .

[13]  Junyi Guo,et al.  Optimal dividend and equity issuance problem with proportional and fixed transaction costs , 2012 .

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

[15]  Lin He,et al.  Optimal financing and dividend control of the insurance company with proportional reinsurance policy , 2008 .

[16]  H. Schmidli,et al.  Optimal dividend strategies in a Cramer–Lundberg model with capital injections and administration costs , 2011 .

[17]  Junyi Guo,et al.  Optimal dividend problem with a nonlinear regular-singular stochastic control , 2013 .

[18]  V. Young.  Equity-Indexed Life Insurance: Pricing and Reserving Using the Principle of Equivalent Utility , 2003 .

[19]  Lin He,et al.  Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs , 2009 .

[20]  Mihail Zervos,et al.  Optimal dividend and issuance of equity policies in the presence of proportional costs , 2008 .

[21]  M. Kaluszka.  Optimal reinsurance under convex principles of premium calculation , 2005 .

[22]  Hailiang Yang,et al.  Optimal risk and dividend control problem with fixed costs and salvage value: Variance premium principle , 2014 .

[23]  W. Fleming,et al.  Controlled Markov processes and viscosity solutions , 1992 .

[24]  Zongxia Liang,et al.  Viscosity solution and impulse control of the diffusion model with reinsurance and fixed transaction costs , 2014 .

[25]  Pricing equity-linked pure endowments via the principle of equivalent utility , 2003 .

[26]  Tak Kuen Siu,et al.  On optimal reinsurance, dividend and reinvestment strategies , 2011 .