| Abstract: | 可以模擬公司整體營運的系統對壽險業者來說是一個很有力的管理工具，因為這樣的系統可以描繪出壽險經營隨機與動態的本質。不過，模擬系統本身是「描述性」的，只能在使用者輸入決策變數的值之後產生可能的結果，無法告訴使用者怎樣的決策變數值才能得到最佳的結果。 這個計畫將應用模擬最佳化的技術於壽險公司的模擬系統，幫助學者與業者瞭解一些壽險經營的基本管理議題。我們將先建構一個壽險公司的模擬系統，這個系統將能模擬公債、公司債、股票、不動產、以及國外投資等各項資產價值的變化。這個系統也將模擬定期死亡險、利率連結型生死合險、投資連結型終身壽險、以及短期傷害險。系統的輸入變數包含資產配置、資本結構、壽險業務的組合、以及業務的成長率等。系統的輸出變數將是所模擬的業主權益、破產機率、以及資本適足率等變數的函數。 然後我們會架構一些模擬最佳化的演算法於壽險公司的模擬系統。我們選擇了三個演算法：基因演算法，演化策略法、以及模擬鍛鍊（simulation annealing）。這些演算法適用於解空間是多峰、不連續、或無法微分的問題，可以避免搜尋時陷入區域性的最佳解。 有了求最佳解功能的壽險公司模擬系統後，我們將開始分析一些壽險經營的基本管理問題，例如：壽險業務的組成、成長率、與槓桿比率等對資產配置的影響。我們也會把這些變數當成決策變數，看看這樣的全公司整體考量能產生多少目標函數值的改進。
A company-wide simulation system is a powerful tool for life insurers in making decisions. It is capable of profiling the stochastic and dynamic nature of life insurance business operations, and it is getting popular around the world. However, a company-wide simulation system is merely a descriptive model. It helps users to know which proposed strategy is better, but fails to tell us what the optimal strategy is. A simulation system without an optimization mechanism is therefore incapable of helping managers maximize the shareholders』 value. This project intends to apply the techniques of simulation optimization to a simulation system of a life insurance company to equip the system with optimization capability. Simulation optimization is the process of determining the values of the controllable input variables that optimize the values of the stochastic output variables generated by a simulation system. The controllable input variables, also called decision variables, in this project will include asset allocation, rebalancing strategies, capital structure, business growth, and business compositions. The output variables, also called the response variables, are a function of the expected value of simulated surplus, insolvency probability, and other concerns of the board (e.g., meeting the capital requirement). We will first build a company-wide simulation system of a life insurance company. The system will model several types of assets and insurance products. Simulated assets include government bonds, corporate bonds, stocks, real estate, and foreign investments. The insurance products considered in this project include non-participating term life insurance, interest-rate-linked endowment, and participating whole life insurance, and personal injury insurance. Although the system is a simplified version of real-world operations, it is complex enough to preclude one from finding optimal decision variables analytically. We then resort to some techniques of simulation optimization, namely global optimization. Global optimization techniques are designed for problems of which the response surface has is multi-modal, discontinuous, and/or non-differentiable. We choose genetic algorithms (GA), evolution strategies (ES), and simulation annealing (SA) to optimize our simulation system. SA is a well-known local search method that was developed to help a search escape from local optimum. GA and ES are two commonly used evolutionary algorithms (EA). EA work on a population of solutions in such a way that poor solutions become extinct while good solutions evolve to reach for the optimum. After equipping a company-wide simulation system with optimization algorithms, we will employ the equipped system to answer several essential questions regarding life insurer management that interest both scholars and managers. For instance, scholars and practitioners wonder how life insurance businesses may affect the asset allocation of life insurers. How will the optimal asset allocation change with the consideration of life insurance businesses? How about the growth rate of life insurance businesses? Shall a rapid-growing insurer adopt different asset allocation strategies from the strategies of matured insurers? How will the leverage ratio of an insurer affect the optimal asset allocation? We can also enlarge our decision variable set to include the growth rate, business compositions, and the leverage ratio to reach the optimal company-wide decisions. |
