SUMMARIES AND CONCLUSIONS

Managing an insurance company is more difficult than managing other types of companies because an insurer faces not only asset risks but also liability risks. The DFA system is a promising tool for the insurer. It takes full account of the static and dynamic relations among asset variables and liability variables. The major output of a DFA system is the distribution ofan insurer’sfuture surplus that can be further used to compare alternative asset allocations, business strategies, and reinsurance arrangements, among others.

Insurance regulators can use a DFA system to perform an early warning analysis as well as set up minimal capital requirements.

The main drawback of the DFA system is the lack of an optimization mechanism.

Users can perform only comparative analysis with no way of knowing what the optimal

strategy is. Simulation optimization is receiving considerable interest in the field of operations research and may be a nice complement to the DFA system. By incorporating optimization features in a DFA system, the DFA system turns from a descriptive model into an operational tool to solve various decision-making problems. The contribution of this paper is coupling a DFA system with a simulation optimization technique and applying the combination to the asset allocation problem of a property-casualty insurance company.

We first built up a simply DFA system in which an insurer underwrites both short-and long-tail businesses short-and invest in four types of assets. Then we formulated the asset allocation problem as a multi-period one instead of a single-period one. A multi-period asset allocation is superior because the accumulation of a sequence of single-period optimal decisions across periods may not be optimal for these periods taken as a whole. We also considered the short-sale constraints faced by insurers when making investments. The capability of solving a constrained multi-period problem illustrates the advantage of

simulation optimization, although we must keep in mind that the found solution as a result of simulation optimization cannot be proved to be the optimum. The simulation optimization technique used in this paper is a generic algorithm.

We successfully incorporated a generic algorithm into a DFA system and performed a search for the optimal asset allocation of a property-casualty insurer in this paper. The resulting asset allocation was a significantly higher value of the objective function compared

to the allocation found from a basic search method. The optimal allocation produced a higher average discounted surplus and a lower ruin probability. Using different sets of random number generated similar values of objective function and demonstrated the

robustness of our coupling across random numbers. The optimal asset allocation is sensitive to the parameters of financial and insurance market models, with the changes being consistent with the differences in the parameters. Therefore, insurance companies that are using or are interested in DFA should learn one of the simulation optimization techniques to equip their DFA systems with optimization features.

References

Andradottir, S., 1998. Simulation Optimization. In: Handbook of Simulation: Principles, Methodology, Advances, Applications, and Practice. Wiley, New York, pp. 307-333.

Back, T., Schwefel, H. P., 1993. An overview of evolutionary algorithms for parameter optimization. Evolutionary Computation 1, 1-23.

Chen, C. L., Vempati, V. S., Aljaber, N., 1995. An application of genetic algorithms for flow shop problems. European Journal of Operational Research 80, 389-396.

Chen, C. L., Neppalli, V. R., Aljaber, N., 1996. Genetic algorithms applied to the continuous flow shop problem. Computers and Industrial Engineering 30, 919-929.

Chen, C. L., Lin, R. H., Zhang, J., 2003. Genetic algorithms for MD-optimal follow-up designs. Computers & Operations Research 30, 233-252.

Coutts, S. M., Devitt, R., 1989. The Assessment of the Financial Strength of Insurance Companies by a Generalized Cash Flow Model. In: Financial Models of Insurance Solvency. Kluwer Academic Publishers, Boston, pp. 1-36.

Cox, J. C., Ingersoll, J. E., Ross, S. A., 1985. A theory of the term structure of interest rates.

Econometrica 53, 385-407.

Cummins, J. D., Grace, M. F., Phillips, R. D., 1999. Regulatory solvency prediction in property-liability insurance: risk-based capital, audit ratios, and cash-flow simulation.

Journal of Risk and Insurance 66, 417-458.

Daykin, C. D., Bernstein, G. D., Coutts, S. M., Devitt, E. R. F., Hey, G. B., Reynolds, D. I. W., Smith, P. D., 1989. The Solvency of a General Insurance Company in Terms of

Emerging Costs. In: Financial Models of Insurance Solvency. Kluwer Academic Publishers, Boston, pp. 87-149.

Daykin, C. D., Hey, G. B., 1991. A Management Model of a General Insurance Company Using Simulation Techniques. In: Managing the Insolvency Risk of Insurance

Companies. Kluwer Academic Publishers, Boston, pp. 77-108.

Daykin, C. D., Pentikainen, T., Pesonen, M., 1994. Practical Risk Theory for Actuaries.

Chapman & Hall, London.

Eshelman, L. J., Schaffer, J. D., 1993. Real-Coded Genetic Algorithms and Interval

Schemata. In: Foundations of Genetic Algorithms. Morgan Kaufmann Publishers, San

Mateo, pp. 187-202.

Fu, M. C., 1994. Optimization via simulation: a review. Annals of Operations Research 53, 199-247.

Keys, A. C., Rees, L. P., 2004. A sequential-design metamodeling strategy for simulation optimization. Computers and Operations Research 31, 1911-1932.

Michalewicz, Z., 1996. Genetic Algorithms + Data Structures = Evolution Programs, 3rd ed.

Springer-Verlag, Berlin.

Paulson, A. S., Dixit, R., 1989. Cash Flow Simulation Models for Premium and Surplus Analysis. In: Financial Models of Insurance Solvency. Kluwer Academic Publishers, Boston, pp. 37-56.

Pentikainen, T., 1988. On the Solvency of Insurers. In: Classical Insurance Solvency Theory. Kluwer Academic Publishers, Boston, pp. 1-48.

Taylor, G., 1991. An Analysis of Underwriting Cycles and their Effects on Insurance Solvency. In: Managing the Insolvency Risk of Insurance Companies. Kluwer Academic Publishers, Boston, pp. 3-76.

Taylor, G. C., Buchanan, R., 1988. The Management of Solvency. In: Classical Insurance Solvency Theory. Kluwer Academic Publishers, Boston, pp. 49-155.

Tekin, E., Sabuncuoglu, I., 2004. Simulation optimization: a comprehensive review on theory and applications. IIE Transactions 36, 1067-1081.

Table 1: The results of the basic research method

1 0 0 0 -72,581,897 351,418,103 0.0306

0.8 0.2 0 0 551,978,871 463,978,871 0.0178

0.8 0 0.2 0 -46,112,487 353,887,513 0.0300

0.8 0 0 0.2 552,303,659 552,303,659 0.0200

0.6 0.4 0 0 637,421,327 605,421,327 0.0192

0.6 0.2 0.2 0 570,938,385 466,938,385 0.0174

0.6 0.2 0 0.2 971,157,610 699,157,610 0.0132

0.6 0 0.4 0 12,156,152 356,156,152 0.0286

0.6 0 0.2 0.2 587,409,029 555,409,029 0.0192

0.6 0 0 0.4 336,229,618 840,229,618 0.0326

0.4 0.6 0 0 280,468,735 776,468,735 0.0324

0.4 0.4 0.2 0 664,738,139 608,738,139 0.0186

0.4 0.4 0 0.2 1,097,049,222 873,049,222 0.0144

0.4 0.2 0.4 0 589,926,635 469,926,635 0.0170

0.4 0.2 0.2 0.2 975,076,921 703,076,921 0.0132

0.4 0.2 0 0.4 865,202,808 1,017,202,808 0.0238

0.4 0 0.6 0 70,408,056 358,408,056 0.0272

0.4 0 0.4 0.2 614,605,036 558,605,036 0.0186

0.4 0 0.2 0.4 379,816,127 843,816,127 0.0316

0.4 0 0 0.6 -1,437,343,176 1,234,656,824 0.0868

0.2 0.8 0 0 -979,818,603 988,181,397 0.0692

0.2 0.6 0.2 0 331,768,042 779,768,042 0.0312

0.2 0.6 0 0.2 920,627,902 1,072,627,902 0.0238

0.2 0.4 0.4 0 707,867,321 611,867,321 0.0176

0.2 0.4 0.2 0.2 1,132,889,250 876,889,250 0.0136

0.2 0.4 0 0.4 996,985,281 1,220,985,281 0.0256

0.2 0.2 0.6 0 585,128,292 473,128,292 0.0172

0.2 0.2 0.4 0.2 1,002,693,284 706,693,284 0.0126

0.2 0.2 0.2 0.4 916,984,155 1,020,984,155 0.0226

0.2 0.2 0 0.6 -262,968,275 1,425,031,725 0.0622

0.2 0 0.8 0 120,775,989 360,775,989 0.0260

0.2 0 0.6 0.2 641,808,556 561,808,556 0.0180

0.2 0 0.4 0.4 423,394,768 847,394,768 0.0306

0.2 0 0.2 0.6 -1,377,259,696 1,238,740,304 0.0854

0.2 0 0 0.8 -4,699,438,942 1,764,561,058 0.1816

0 1 0 0 -3,230,097,737 1,249,902,263 0.1320

0 0.8 0.2 0 -881,219,802 990,780,198 0.0668

0 0.8 0 0.2 192,104,867 1,304,104,867 0.0478

0 0.6 0.4 0 351,750,776 783,750,776 0.0308

0 0.6 0.2 0.2 948,987,876 1,076,987,876 0.0232

0 0.6 0 0.4 608,774,850 1,456,774,850 0.0412

0 0.4 0.6 0 727,242,728 615,242,728 0.0172

0 0.4 0.4 0.2 1,137,275,044 881,275,044 0.0136

0 0.4 0.2 0.4 1,017,769,551 1,225,769,551 0.0252

0 0.4 0 0.6 -153,875,069 1,662,124,931 0.0654

0 0.2 0.8 0 604,121,085 476,121,085 0.0168

0 0.2 0.6 0.2 1,022,434,859 710,434,859 0.0122

0 0.2 0.4 0.4 953,078,642 1,025,078,642 0.0218

0 0.2 0.2 0.6 -187,400,811 1,428,599,189 0.0604

0 0.2 0 0.8 -3,183,750,687 1,968,249,313 0.1488

0 0 1 0 131,373,027 363,373,027 0.0258

0 0 0.8 0.2 661,117,051 565,117,051 0.0176

0 0 0.6 0.4 451,314,002 851,314,002 0.0300

0 0 0.4 0.6 -1,309,777,975 1,242,222,025 0.0838

0 0 0.2 0.8 -4,639,208,243 1,768,791,757 0.1802

0 0 0 1 -8,421,281,758 2,482,718,242 0.2926

Figure 1: Classification of optimization methodologies

Figure 2: The simulated short rate statistics along with time

Optimization Problems