Optimal Expected Utility of Wealth for Two Dependent Classes of Insurance Business

ABSTRACT

We consider a modified version of the
classical Cramer-Lundberg risk model. In particular, we assume two classes of
insurance business dependent through the claim number process *N*_{i}, *i*=1,2: we consider that the number
of claims is generated by a bivariate Poisson distribution (*N*_{1}, *N*_{2}). We also
consider the presence of a particular kind of reinsurance contract, supposing
that the first insurer concludes an Excess of Loss reinsurance limited by *L*_{i}, *i*=1,2, with retention limits *b*_{i}, *i*=1,2, for the respective classes of
insurance business. The aim of this paper is to maximize the expected utility
of the wealth of the first insurer, having the retention limits as decision
variables. We assume an exponential utility function and, fixed *L*_{i}, *i*=1,2, we discuss optimal *b*_{i}, *i*=1,2.

Cite this paper

C. Gosio, E. Lari and M. Ravera, "Optimal Expected Utility of Wealth for Two Dependent Classes of Insurance Business,"*Theoretical Economics Letters*, Vol. 3 No. 2, 2013, pp. 90-95. doi: 10.4236/tel.2013.32015.

C. Gosio, E. Lari and M. Ravera, "Optimal Expected Utility of Wealth for Two Dependent Classes of Insurance Business,"

References

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[1] H. Albrecher and O. J. Boxma, “A Ruin Model with Dependence between Claim Size and Claim Intervals,” Insurance: Mathematics and Economics, Vol. 35, No. 2, 2004, pp. 245-254. doi:10.1016/j.insmatheco.2003.09.009

[2] H. Albrecher, C. Costantinescu and S. Loisel, “Explicit Ruin Formulas for Models with Dependence among Risks,” Insurance: Mathematics and Economics, Vol. 48, No. 2, 2011, pp. 265-270. doi:10.1016/j.insmatheco.2010.11.007

[3] M. Boudreault, H. Cossette, D. Landriault and E. Marceau, “On a Risk Model with Dependence between Interclaim Arrivals and Claim Sizes,” Scandinavian Actuarial Journal, No. 5, 2006, pp. 265-285. doi:10.1080/03461230600992266

[4] H. Cossette, E. Marceau and F. Marri, “Analysis of Ruin Measures for the Classical Compound Poisson Risk Model with Dependence,” Scandinavian Actuarial Journal, No. 3, 2010, pp. 221-245. doi:10.1080/03461230903211992

[5] D. Landriault, “Constant Dividend Barrier in a Risk Model with Interclaim-Dependent Claim Sizes,” Insurance: Mathematics and Economics, Vol. 42, No. 1, 2008, pp. 31-38. doi:10.1016/j.insmatheco.2006.12.002

[6] R. S. Ambagaspitiya, “On the Distribution of a Sum of Correlated Aggregate Claims,” Insurance: Mathematics and Economics, Vol. 23, No. 1, 1998, pp. 15-19. doi:10.1016/S0167-6687(98)00018-3

[7] R. S. Ambagaspitiya, “Compound Bivariate Lagrangian Poisson Distributions,” Insurance: Mathematics and Economics, Vol. 23, No. 1, 1998, pp. 21-31. doi:10.1016/S0167-6687(98)00020-1

[8] R. S. Ambagaspitiya, “Aggregate Survival Probability of a Portfolio with Dependent Subprtfolios,” Insurance: Mathematics and Economics, Vol. 32, No. 3, 2003, pp. 431-443. doi:10.1016/S0167-6687(03)00131-8

[9] J. Cai and W. Wei, “Optimal Reinsurance with Positively Dependent Risks,” Insurance: Mathematics and Economics, Vol. 50, No. 1, 2012, pp. 57-63. doi:10.1016/j.insmatheco.2011.10.006

[10] M. L. Centeno, “Dependent Risks and Excess of Loss Reinsurance,” Insurance: Mathematics and Economics, Vol. 37, No. 2, 2005, pp. 229-238. doi:10.1016/j.insmatheco.2004.12.001

[11] G. Wang and K. C. Yuen, “On a Correlated Aggregate Claims Model with Thinning-Dependence Structure,” Insurance: Mathematics and Economics, Vol. 36, No. 3, 2005, pp. 456-468. doi:10.1016/j.insmatheco.2005.04.004

[12] K. C. Yuen, J. Guo and X. Wu, “On a Correlated Aggregate Claims Model with Poisson and Erlang Risk Processes,” Insurance: Mathematics and Economics, Vol. 31, No. 2, 2002, pp. 205-214. doi:10.1016/S0167-6687(02)00150-6

[13] K. C. Yuen, J. Guo and X. Wu, “On the First Time of Ruin in the Bivariate Compound Poisson Model,” Insurance: Mathematics and Economics, Vol. 38, No. 2, 2006, pp. 298-308. doi:10.1016/j.insmatheco.2005.08.011

[14] G. E. Willmot and J. K. Woo, “On the Analysis of a General Class of Dependent Risk Processes,” Insurance: Mathematics and Economics, Vol. 51, No. 1, 2012, pp. 134-141. doi:10.1016/j.insmatheco.2012.03.007

[15] C. Hipp, “Stochastic Control with Applications in Insurance,” Stochastic Methods in Finance, Lecture Notes in Mathematics, Vol. 1856, 2004, pp. 127-164. doi:10.1007/978-3-540-44644-6_3

[16] L. Johnson, S. Kotz and N. Balakrishnan, “Discrete Multivariate Distributions,” Wiley, New York, 1997.