本文延續Huang(2004, 2008)的研究，將單期與多期挹注資金的資產負債管理議題專化於DC確定提撥退休金制度上，其研究將問題化成二次函數，以一般化最小平方法(Generalized least square, GLS)求出具有唯一解特性的決策變數，利用的軟體求解速度相當快，能有效率地一次找出多項資產配置比例。 本研究引入三種投資模型及其薪資模型，分別是Wilkie(1995)模型、MacDonald and Cairns(2007)模型、Huang and Cairns(2006)及Li(2009)，以蒙地卡羅模型模擬出各投資標的年報酬率與薪資水準，並利用這些預期的模擬值在負債目標控制為隨機成長或固定比例成長下，找出最適投資比例、每期挹注的額度與提撥比例。 最適配置為了解決下方風險(downside risk)問題，在允許限定風險容忍度下去最大化投資績效，本研究將目標函數加入衡量報酬項，依據員工希望的報酬，討論此項權重如何最適。亦加入交易成本項以反映實務情況，此投資總交易成本為權重的函數，於足夠支付交易成本的前提下找出權重最小值。 / In this study, the simulation of the return for each investment and wage pattern is via introduction of three investment model and their wage model, namely, Wilkie (1995) model, MacDonald and Cairns (2007) model, Huang and Cairns (2006) model and Li (2009), by using Monte Carlo simulation. The optimal contribution rate of investments, the amount of injection of each period, and income replacement ratio are determined when simulation is targeted in the balance control for the random growth or growth under a fixed rate of liabilities. The asset-liability management of single-period and multi-period injection of funds is specialized in the Defined contribution plan (DC), which is the extension of Huang’s (2004, 2008) study. Huang’s research transforming his argument into a quadratic function to generalized least squares method (GLS) having a unique solution to derive the decision-making variables. This method can efficiently find a set of allocation by software at a fairly rapid speed. The optimal allocation is to maximize investment performance subject to a limited risk had to tolerance for deal with downside risk. This study ameliorates the objective function by adding a constant term, which does not affect the investment decision-making variable. This new generalized least squares method use a constant represented as a weight, which is based on the desire asset of the employee. This study also takes transaction costs into consideration to reflect the practical situation. The total transaction costs are the function of the weight introduced into the new objective function. The minimum of weight can be reached when the goal is set to be sufficient to cover the transaction costs

本文主要是針對保險業及退休基金的資產負債管理議題為研究重心，延續Huang (2004)的研究，其研究是以理論求解的方式求出多期最適資產配置的唯一解，而其研究也衍生出兩個議題：首先是文中允許資產買賣空;再者其模型僅解決單期挹注資金的問題，而不考慮多期挹注資金。但這對於實際市場操作上會有一些的問題。因此本文延續了其研究，希望解決這兩個議題，讓模型更能解出一般化的資產負債管理問題。 本文所選擇的投資的標的是以一般退休基金與保險業所採用，分別是短債(short-term bonds)、永續債卷(consols)、指數連結型債券(index-linked gilts(ILG))、股票(equity)為四種投資標的，以蒙地卡羅模型模擬出4000組Wilkie 投資模型(1995)下的四種標的年報酬率以及負債年成長率，利用這些預期的模擬值找出最適的投資比例以及應該挹注的金額。而本文主要將問題化為決策變數的二次函數，並以一般化最小平方法(generalized least square,GLS)來求出決策變數，而用此方法最大的優點在於一般化最小平方法具有唯一解，且在利用軟體求解的速度相當快，因此是非常有效率的。本文探討的問題可以分成兩個部分。我們首先討論「單期挹注資金」的問題，只考慮在期初挹注資金。接著我們考慮「多期挹注資金」的問題，是在計畫期間內能將資金分成多期投入。兩者都能將目標函數化為最小平方的形式，因此本文除了找出合理的資產配置以及解決多期挹注資金的問題之外，也將重點著重於找一個能快速且精準的方法來解決資產配置的問題。 / This paper deals with the insurance and pension asset liability management issue. Huang (2004) derives a theoretical close solution of multi-period asset allocation. However, there are two further problems in his paper. First, short selling is allowable. Second, multi-period investing is not acceptable. These two restrictions sometimes are big problems in practice. This paper extends his paper and releases these two restrictions. In other words, we intend to find a solution of multi-period asset allocation so that we can invest money and change proportion of investment in each period without problems of short selling. In this paper, we use the standard asset classes used by pension or insurance funds such as short-term bonds, consols, index-linked gilts and equities. We generate thousand times of Monte Caro simulations of Wilkie investment model (1995) to predict future asset returns. Furthermore, in order to improve time-efficiency and accuracy, we derive a quadratic objective function and obtain a unique solution using sequential quadratic programming.