責任準備金的風險管理是人壽保險公司營運的重要課題之一，其牽涉到保單現金流量的數階動差及分佈之估計，為此我們必須清楚的設定隨機脫退和隨機利率模型，並將保單之重要特性—利率敏感性現金流量納入考慮，否則將誤導保險公司過度規避利率風險及高估其破產的危險性。

本文採用蒙地卡羅模擬法進行責任準備金的模擬，在模擬模型中考慮三個風險因子：死亡率風險、利率風險和解約率風險。透過死亡率的變異數估計死亡率風險對責任準備金的影響；透過隨機利率模型估計隨機利率對責任準備金的影響；於解約率模型中考慮利率與解約率的關係，估計解約率對責任準備金的影響；當中並將隨機利率模型與解約率模型的參數風險納入考慮。最後，將五個險種的現金流量加權平均，以建構保險商品組合，而具有最小的最大分散（maximum dispersion）的保險商品組合即為最佳商品組合，所謂責任準備金的最大分散即責任準備金之第95個百分位數與其平均數之差距。

由模擬結果發現，保險公司應密切注意其責任準備金之利率風險管理，但這並不表示保險公司可忽視解約率風險對責任準備金的影響，而過度規避利率風險，此模擬結果幫助保險公司評估其業務之風險。

One of the major topics in insurance companies’ operations is the risk management of the reserves. Sound risk management of reserves involves the estimation of the moments and distribution of cash flows associated with sold policies. To estimate the moments or the distribution of future cash flows, one must model stochastic decrements and stochastic discount rates explicitly. Besides, one must consider an important feature of insurance policies: future cash flows may be interest-rate-sensitive. Ignorance of such characteristic may mislead the insurer to over-hedge the interest rate risk and jeopardize the solvency of insurers.

In this paper we use Monte Carlo simulation to estimate reserve. We identify three risk factors embedded in life insurers’ reserves in our simulation model: mortality risk, interest rate risk, and lapse rate risk. We use the mortality risk to decide the reserve from the variances of mortality rates. We choose a term structure to decide the reserve from the interest rate risk. Furthermore, we incorporate lapse rate risk into the decision of reserve by recognizing the relationship between lapse rates and interest rates. We also estimate the parameter risk associated with the parameter estimation errors in the term structure model and the lapse rate model. Finally, we construct insurance portfolios by summing weighted cash flow of five insurance policies. According to the minimum maximum dispersion, we intend to find the optimal portfolio and identify that the maximum dispersion of the distribution of terminal reserve is the difference between reserve’s 95th percentile and mean.

We find that the maximum dispersion generated from mortality risk is insignificant while maximum dispersion from interest rate risk is substantial. This result is consistent with the observation that life insurers suffer more from the interest rate risk than from the mortality rate risk. The marginal contribution of lapse rate risk to the maximum dispersion, surprisingly, is negative. One possible reason is that the duration of the reserve decreases if policies lapse and lower duration means less interest rate related risk. This seemingly surprising result implies that we would overestimate the maximum dispersion if we neglect the lapse rate risk. We also find that the parameter risks of the interest rate model and the lapse rate model are significant. Our findings suggest that life insurers should pay close attention to interest rate risk management. However, be careful not to neglect the effect of lapse rate and over-manage the interest rate risk. In addition, insurers should be aware of the significance of parameter estimation risks in pricing models. The results of portfolios show that the maximum dispersion is deeply affected by the considered risk and the diversification effect. Our results can help life insurers to access the riskiness of their business.

Albizzati, Marie-Odile and Helyette Geman, 1994, Interest Rate Risk Management and Valuation of the Surrender Option in Life Insurance Policies, Journal of Risk and Insurance, 61: 616-637.
American Council of Life Insurance, 1999, The Life Insurance Fact Book (Washington D.C.: ACLI)
Babbel, David F., 1995, Asset-Liability Matching in the Life Insurance Industry, The Financial Dynamics of the Insurance Industry (New York: IRWIN Professional Publishing)
Beekman, John A. and Clinton P. Fuelling, 1990, Interest and Mortality Randomness in Some Annuities, Insurance: Mathematics and Economics, 9: 185-196.
Beekman, John A. and Clinton P. Fuelling, 1991, Extra Randomness in Certain Annuity Models, Insurance: Mathematics and Economics, 10: 275-287.
Beekman, John A. and Clinton P. Fuelling, 1993, One Approach to Dual Randomness in Life Insurance, Scandinavian Actuarial Journal, 2: 173-182.
Bowers, Newton L., Hans U. Gerber, James C. Hickman, Donald A. Jones, and Cecil J. Nesbitt, 1986, Actuarial Mathematics (Schaumburg, Illinois: Society of Actuaries).
Briys, Eric and Francois de Varenne, 1997, On the Risk of Insurance Liabilities: Debunking Some Common Pitfalls, Journal of Risk and Insurance, 64: 673-694.
Frees, Edward W., 1990, Stochastic Life Contingencies with Solvency Considerations, Transaction of the Society of Actuaries, 42: 91-129.
Giaccotto, Carmelo, 1986, Stochastic Modeling of Interest Rates: Actuarial vs. Equilibrium Approach, Journal of Risk and Insurance, 53: 435-453.
Grosen, Anders, and Peter Lochte Jorgensen, 1997, Valuation of Early Exercisable Interest Rate Guarantees, Journal of Risk and Insurance, 64: 481-503.