當產險公司需要同時兼顧競爭力並免於破產時，適當的資產配置就是一項相當重要的決策。然而採用均數-變異數分析(mean‐variance analysis)將受到許多限制，而動態控制理論則是難以實作，因此，我們提出一個新的解決方法。這個方法主要係應用模擬最佳化的演算法，例如基礎的基因演算法(basic genetic algorithm, GA)，多階層演化策略(multi-phase evolutionary strategies, MPES)及多階層基因演算法(multi-phase genetic algorithm, MPGA)等並結合模擬模型，來求解保險公司之資產配置的問題。首先我們建立投資市場及保險業務市場的模擬模型，之後再利用本研究所發展出新的最佳化演算法來搜尋最佳的資產配置。在實務上無法實現的多期投資策略，在我們的研究架構下得以被採用，並且在比較求解結果下，多期投資策略(reallocation strategies)較定額投資策略(re‐balancing strategies)有顯著較佳的績效。在兼顧保險公司投資收益並避免破產的目標函數下，我們所提出的研究方法已證明可以用來協助保險公司建立較佳的資產配置。 / Proper asset allocations are vital for property‐casualty insurers to be competitive and remain solvent. However, popular mean‐variance analysis is limited while dynamic control theory is difficult to implement. We thus propose to apply simulation optimizations such as basic genetic algorithm (GA), multi‐phase evolutionary strategies (MPES) and multi‐phase genetic algorithm (MPGA) to the asset allocation problems of the insurers. We first construct a simulation model of the property‐casualty insurer and then develop simulation optimization techniques to search optimal investment strategies upon the simulation results. The resulted reallocation strategies perform better than re‐balancing strategies used in practice with significant margins. Therefore, our proposal researches can be used to assist insurers to construct better asset allocations.

本文結合動態財務分析（Dynamic Financial Analysis, DFA）與演化策略演算法(Evolution Strategy, ES)找尋產險公司最佳的投資比率。本文模擬產險公司的25年的營運情形，將各資產價格變化以隨機模型建構的概念帶入，加入損失分配並考慮多重期間的資產配置比率重分配(re-allocation)等條件，在建立目標方程式後，運用演化策略演算法求得最佳的資產配置比率。 / In the research, the tools we take are the dynamic financial analysis( DFA ) system and the evolution strategy algorithm( ES ), which can be used to find the best investment ratio for insurance companies. The whole content of this article demonstrates the condition of property-casualty insurance companies in the 25 years. It takes place of the change of prices in every item of the asset by some kind of stochastic models, then, takes notice of the distribution of loss and re-allocation, sets a objective function for the goal to find the best ratio of the asset allocation by ES.

過去的文獻中，資產配置的方法不外乎效率前緣、動態資產配置等方式，但是，單獨針對銀行探討的文章並不多見，所以本文的貢獻在於單獨針對銀行的資產配置行為進行研究，希望能利用『演化策略演算法』，進行『模擬最佳化』來解決銀行資產配置的問題。基本上這個方法是由兩個動作結合而成，先是模擬，再來尋求最佳解。所以，資產面我們選擇了現金、債券、股票、不動產四項標的，而負債面則模擬了定存、活存與借入款這三項業務，然後透過重複執行模型的方式來求出最適解。並與單期資產配置方法下的結果作一比較，發現運用演化策略演算法有較佳的結果，此外，在不同的亂數下，仍具有良好的穩健性，可作為一般銀行經理人參考之用。 / We focus on the bank’s asset allocation problem in this thesis. We use simulation optimization to solve the problem by evolution strategy, which is relatively new in the financial field. Simulation optimization consists of two steps: simulate numerous situations and search for the optimal asset portfolios. In the simulation, we set up four assets, including cash, bond, stock, and real estate and three business lines, including demand deposits, time deposits, and borrowings. Then we search for the optimal solution by running the ES algorithm. The results show that simulation optimization generates better results than one-period asset allocation. Furthermore, the evolution strategy method generates similar results using different random numbers.

本研究的第一部份是利用有效存續期間與有效凸性來衡量人壽保險人的利率風險。我們發現Tsai (2009)指出的壽險保單準備金之有效存續期間結構並非一般化的結果。當長期利率水準高於保單預定利率及保單解約率敏感於利差時，準備金之有效存續期間會呈現與Tsai (2009)相反的結構。我們進一步發現準備金之有效凸性會亦有可能呈現負值，且不易依照保單到期期限歸納出一般化的結構。負值的有效凸性起因於準備金並非利率的單調函數，且準備金與利率的函數關係隨保單到期期限而不同。我們的研究結果可以幫助人壽保險人執行更為精確的資產負債管理。 本研究的第二部分是利用模擬最佳化的方法，幫助銷售傳統壽險保單的保險人求解出適切的業務槓桿與資產配置策略。我們假設保險人在考量破產機率與報酬率的波動之下，將資本與淨保費收入投資於資本市場中，以追求較高的業主權益報酬率。以業務槓桿與資產配置相互影響為前提，我們求解出適切的業務槓桿與多期資產配置策略，並分析在不同的業務槓桿之下，保險人多期資產配置的差異。 / In the first part of this doctoral dissertation, we focus on a proper measurement on interest rate risk of life insurer’s liabilities, policy reserves, by incorporating the general effective duration and effective convexity measures. Tsai (2009) identified a term structure of the effective durations of life insurance reserves. We find that his results are not general. When the long-run mean of interest rates is higher than the policy crediting rate and the surrender rate is sensitive to the spread, the term structure would exhibit an opposite pattern to the one in Tsai (2009). We further find that the effective convexities might be negative and the term structure of the effective convexities exhibits no general pattern. The irregularities originate from negative effective convexities result from the relationship between mean reserves and initial short rate for different years to maturity. Our results can help life insurers to implement more accurate asset-liability management. In the second part, we analyze asset allocation and leverage strategies for a life insurer selling traditional insurance products by using a simulation optimization method. We assume that an insurer invests equity capital (from its shareholders) and premiums it receives from policyholders by choosing a portfolio intended to maximize the annual return of equity minus the penalty of insolvencies and risks. We regard the leverage as an internal factor in asset allocation. Based on these assumptions, we get a promising multiple-periods asset allocation and leverage, besides analyzing how leverage affects asset allocation strategies.