勞工退休金條例的實施喚醒國人對退休後生活的重視，開始著重退休財務規劃。確定提撥制下，提撥期間退休準備金之運用深深影響退休時之帳戶金額，對員工影響甚鉅，故資金運用乃是由員工自行決定，投資風險由員工承擔，而投資報酬率對退休所得替代率影響甚鉅，提升報酬率能讓員工退休時有足夠的退休金，當考量退休金能有抗通貨膨脹風險時，更需要較高的報酬率來避免通貨膨脹風險。 本研究採用隨機投資模型模擬股票、債券及兩年期定存報酬率，運用不同投資策略，衡量各種可能投資組合之投資績效與風險，並進一步設計各投資策略之生命週期投資模式，以期分析多期投資策略是否有較大之報酬率、較小之風險。本研究建立最適投資策略之目標函數，供投資者選擇適用之目標函數，在設定控制變數下，尋找最適資產配置。 在不考慮生命週期策略時，CM投資策略最為有效率，且單位風險報酬最高，CPPI則無論投資組合如何配置，都具有高風險高報酬之特性。比較生命週期時，35年期投資期間，TIPP生命週期投資策略較TIPP為佳，而BH生命週期在35年與20年投資期間有較BH有效率之現象。當高風險投資標的變異大時，不宜採用高風險之投資組合，會造成高風險低報酬之情形。另投資者可以根據本研究之最適投資策略設定，選擇最符合自身風險之最佳資產配置策略。

採用風險值取代標準差來衡量投資組合的下方風險，除了更符合投資人的對風險的態度，也更貼近目前金融機構多以風險值作為內部控管工具的情形。但除了風險的事後衡量，本篇論文希望能夠事前積極地控制投資組合風險值，求得最適投資組合的各資產配置權重。故本篇論文研究方法採用了Rockafellar and Uryasev.(2000)的極小條件風險值最適投資組合模型先建立Mean-CVaR效率前緣，並將此效率前緣上的投資組合風險以風險值衡量，再應用電腦上的探索方法進一步求得風險值更低的投資組合，逼近求得Mean-VaR效率前緣，最後利用Mean-VaR效率前緣採用Campbell，Huisman與Koedijk(2001)模型求得控制風險值下的最適投資組合。 在實證分析上，本篇論文採用國內三檔股票為標的，首先在實證標的資產報酬檢定為非常態分配下，使用歷史模擬法，以資產實際非常態報酬分配估計VaR，驗證了使用本篇論文研究方法極小CVaR投資組合與探索方法，可以適當逼近真實的Mean-VaR效率前緣。再者研究比較不同信賴水準、不同資產報酬分配假設與不同權重產生方式下的Mean-VaR效率前緣與Ｍean- 效率前緣效果差異，最後求得控制風險值下的最適投資組合。 / In contrast to the role of variance in the traditional Mean-Variance framework, in this thesis we introduce Value-at-Risk (VaR) as a shortfall-constraint into the portfolio selection decision. Doing so is much more in fitting with individual perception to risk and in line with the constraints which financial institutes currently face. However, mathematically VaR has some serious limitations making the portfolio selection problem difficult to attain optimal solution. In order to apply VaR to ex ante portfolio decision, we use the closely related tractable risk measure Conditional Value-at-Risk (CVaR) in this thesis as a proxy to find efficient portfolios. We utilize linear programming formulation developed by Rockafellar and Uryasev(2000) to construct a Mean-CVaR efficient frontier. Following which the VaR of resulting portfolios in the Mean-CVaR efficient frontier is reduced further by a simple heuristic procedure. After constructing an empirical Mean-VaR efficient frontier that can be proven an useful approximation to the true Mean-VaR efficient frontier, the Campbell, Huisman and Koedijk(2001) model is used to find the optimal portfolio. Three Taiwan listing stocks are used to build the Mean-VaR efficient frontier in the empirical study. And the Mean-VaR efficient frontier of different confident levels, under different asset return assumptions, and different optimal portfolio selection models are compared and results analyzed.

關於Merton (1969) 最適投資組合策略問題，所考慮之投資情境為：一個將其財富資金安排配置於風險性資產(各類證券)與無風險短期現金部位之投資人，在給定此投資人心目中財富效用函數之前提下，希望事先決定出投資組合之最適投資權重(策略)，藉此達成在投資期滿時極大化財富效用之期望值。基於Merton (1974) 公司價值觀點，具有違約風險之證券(公司債與股票)乃是公司價值之衍生性商品，無法以傳統資產配置對股票與債券部位採取現貨方式處理最適投資策略，在此必需同時結合財務工程處理衍生性金融商品計價與避險之技術來解決。本研究利用Kron & Kraft (2003) 彈性求解法來針對市場是否有投資限制、債券提前違約、到期違約及利率隨機與否等假設，基於不同投資組合情境分析來最適投資部位策略。本研貢獻和究創新突破之處在於特別探討公司違約時，債券投資人不再享有全部公司殘值之求償權，此時股東亦享有部份比例之求償權，違約後之公司殘值將由債券投資人與股東兩者比例共分之特殊情境下，對數型態財富效用之投資人對於提前違約風險之接受度高於到期違約風險，若一般情境(股東無任何求償權)則為相反。此外亦特別提供最適成長投資組合之動態避險策略封閉解，藉以提供投資人面臨企業違約風險時應制定之投資決策與動態調整，使本研究臻至週延與實用。 / Under the Merton (1969) optimal portfolio problem, we only consider the specific investor, whose wealth utility follows the type of logarithm function; wants to maximize the expected value of the terminal wealth utility through determine the optimal investment strategy in advance. He divides his wealth into the riskless asset and risky assets such as the money market account and the various-risky securities issued by the corporate. Based on the Merton firm value framework (1974), the defaultable securities, such as the corporate bonds and stocks, are the derivatives instruments of the firm value. It will be inappropriate if we deal with this optimal portfolio problem under the original methods. Therefore, we need to handle this optimal asset allocation problem through the pricing, valuation and hedging techniques from the financial engineering simultaneously. This study apply the elasticity approach to portfolio optimization (EAPO, Kraft ,2003) to solve the optimal portfolio strategy under various scenarios, such as the market contains the investment constrain or not, intermediate default risks, mature default risk, interest rate risky under the stochastic process. The innovation and contribution of this paper are especially breaking the common setting and analysis the optimal-growth-portfolio strategy under the special scenario. In the common setting, as soon as the default event occurs, the residual firm value will be claimed by the corporate bondholders with fully proportion and the stockholder cannot share any residual value. Oppositely, the stockholder will be able to share the residual firm value proportionally with the corporate bondholder together under the so-called special scenario. We found that the investor would have higher acceptance of the premature default risk than the mature default risk in the special scenario. This phenomenon will be reversed under the common scenario. Furthermore, in order to make this study more completely and useful, we do not only illustrate the optimal investment strategy but also provide the closed-formed solution of the dynamic hedge strategy of the risky position, composed by the defaultable securities. This could help the optimal-growth-portfolio-oriented investor to make investment decision while they face the firm value downward decreasing.

本研究顯著地發展時間轉換Lévy過程在最適投資組合的運用性。在連續Lévy過程模型設定下，槓桿效果直接地產生跨期波動度不對稱避險需求，而波動度回饋效果則透過槓桿效果間接地發生影響。另外，關於無窮跳躍Lévy過程模型設定部分，槓桿效果仍扮演重要的影響角色，而波動度回饋效果僅在短期投資決策中發生作用。最後，在本研究所提出之一般化隨機波動度不對稱資產報酬動態模型下，得出在無窮跳躍的資產動態模型設定下，擴散項仍為重要的決定項。 / This study significantly extends the applicability of time-changed Lévy processes to the portfolio optimization. The leverage effect directly induces the intertemporal asymmetric volatility hedging demand, while the volatility feedback effect exerts a minor influence via the leverage effect under the pure-continuous time-changed Lévy process. Furthermore, the leverage effect still plays a major role while the volatility feedback effect just works over the short-term investment horizon under the infinite-jump Lévy process. Based on the proposed general stochastic asymmetric volatility asset return model, we conclude that the diffusion term is an essential determinant of financial modeling for index dynamics given infinite-activity jump structure.