This study tackled portfolio selection problem for an insurer as well as a
reinsurer aiming at maximizing the probability of survival of the Insurer and
the Reinsurer, to assess the impact of proportional reinsurance on the survival
of insurance companies as well as to determine the condition that would warrant
reinsurance according to the optimal reinsurance proportion chosen by the
insurer. It was assumed the insurer’s and the reinsurer’s surplus processes
were approximated by Brownian motion with drift and the insurer could purchase
proportional reinsurance from the reinsurer and their risk reserves followed
Brownian motion with drift. Obtained were Hamilton-Jacobi-Bellman (HJB)
equations which solutions gave the optimized values of the insurer’s and the
reinsurer’s optimal investments in the risky asset and the value of the
discount rate that would warrant reinsurance as a ratio of their portfolio weights
in the risky asset.
Cite this paper
Ihedioha, S. A. and Osu, B. O. (2015). Optimal Portfolios of an Insurer and a Reinsurer under Proportional Reinsurance and Power Utility Preference. Open Access Library Journal, 2, e2033. doi: http://dx.doi.org/10.4236/oalib.1102033.
Gerber, H.U. (1979) An
Introduction to Mathematical Risk Theory. S S Huebner
Foundation Monographs, University of Pensylvama Waters H,
1979, Excess of Loss Reinsurance Limits, 37-43.
Schmidli, H. (2002) On Minimizing the Ruin Probability by Investment and Reinsurance. Annals of Applied Probability, 12, 890-907. http://dx.doi.org/10.1214/aoap/1031863173
Taksar, M.I. and Markussen, C. (2003) Optimal Dynamic Reinsurance Policies for Large Insurance
Portfolios. Finance and Stochastics, 7, 97-121. http://dx.doi.org/10.1007/s007800200073
Browne, S. (1995) Optimal
Investment Policies for a Firm with a Random Risk Process: Exponential
Utility and Minimizing the Probability of Ruin. Mathematics of Operations Research, 20, 937-958. http://dx.doi.org/10.1287/moor.20.4.937
Liu, C.S. and Yang, H. (2004) Optimal
Investment for an Insurer to Minimize Its Probability of Ruin. North American Actuarial Journal, 2, 11-31. http://dx.doi.org/10.1080/10920277.2004.10596134
Castillo, M.T. and
Parrocha, G. (2003) Stochastic Control Theory for Optimal Investment. Working
Paper, Department of Actuarial Studies, University of New South Wales, Sydney.
Irgens, C. and Paulsen, J. (2004) Optimal Control of Risk Exposure, Reinsurance and Investments
for Insurance Portfolios. Insurance, Mathematics and Economics, 35, 21-51. http://dx.doi.org/10.1016/j.insmatheco.2004.04.004
Paulsen, J., Kasozi, J. and
Steigen, A. (2005) A Numerical Method to Find the Probability of Ultimate
Ruin in the Classical Risk Model with Stochastic Return on Investments.
Kasumo, C. (2011) Minimizing
Probability of Ultimate Ruin by Proportiona Reinsurance and
Investment. Msc Dissertation, University of Dar es salaam, Dar es
salaam.
Danping,
L.I. (2015) Optimal Investment Problem for an Insurer and a Reinsurer under the
Proportional Reinsurance. WSEAS Transactions on
Mathematics, 14, 20-35.
Osu,
B.O. and Ihedioha, S.A. (2012) Optimal Portfolio Selection for Pension Funds with Variable Rate
of Return and Transaction Costs: Finite Horizon Case. Global Journal of Pure and AppliedMathematics, 8, 275-286.
Osu, B.O., Ihedioha,
S.A. andAdindu-Dick, J.I. (2014) On the
Survival of Insurance Company’s Investment with Consumption
under Power and Exponential Utility Functions. American Journal of Applied Mathematics, 2, 8-13. http://dx.doi.org/10.11648/j.ajam.20140201.12
Wokiyi, D. (2012) Maximizing
Investment Returns of an Insurance Company While Minimizing the Probability of
Ruin. Master’s Thesis, University of Dar-es-Salam, Dar es salaam, 1-60.
Nie, M. (2010)
Optimal Investment Policy for Pension Funds with Transaction Costs: The Finite
Horizon. Master’s Thesis, Center Graduate School, Finance, Tilburg, 1-49.