The selection of investment strategies and managing investment funds via employing portfolio insurance methods play an important role in asset liability management. Insurance strategies are designed to limit downside risk of portfolio while allowing some participation in potential gain of upside markets. In this thesis, we provide an extensive overview and investigation, particularly on the two most prominent portfolio insurance strategies: the Constant Proportion Portfolio Insurance (CPPI) and the Option-Based Portfolio Insurance (OBPI). The aim of the thesis is to examine, analyze and compare the portfolio insurance strategies in terms of their performances at maturity, via some of their statistical and dynamical properties, and of their optimality over the maximization of expected utility criterion. This thesis presents the financial market model in continuous-time containing no arbitrage opportunies, the CPPI and OBPI strategies with definitions and properties, and the analysis of these strategies in terms of comparing their performances at maturity, of their statistical properties and of their dynamical behaviour and sensitivities to the key parameters during the investment period as well as at the terminal date, with both formulations and simulations. Therefore, we investigate and compare optimal portfolio strategies which maximize the expected utility criterion. As a contribution on the optimality results existing in the literature, an extended study is provided by proving the existence and uniqueness of the appropriate number of shares invested in the unconstrained allocation in a wider interval.

本文利用模擬最適化（Simulation Optimization）的技術，來找出適合投資人之最佳資產配置。模擬最適化係為一種將決策變數輸入而使其反應變數得到最佳化結果之技術，在本篇中，決策變數為各種投資標的之資產配置，而反應變數則為投資結果之預期報酬與標準差，模擬最適化可視為一種在可行範圍內尋求最佳解之過程。本篇中模擬最適化之方法係採演化策略法，最適化問題則為具放空限制之多期架構。我們亦進一步與各種傳統的投資保險策略比較，包括買入持有策略（Buy-and-Hold）、固定比例策略（Constant Mix）、固定比例投資保險策略（Constant Proportion Portfolio Insurance）及時間不變性投資組合保險策略（Time-Invariant Portfolio Protection），以驗證模擬最適化的有效性，並以多種評估指標來衡量各種策略績效之優劣。 由實證結果發現，利用模擬最適化求解出每月的最適資產配置，雖然造成每期因資金配置比例變動而提高波動性，另一方面卻能大幅的增加報酬率。整體而言，模擬最適化技術的確能夠有效提升投資績效，使得最終財富增加，並且得到較大的夏普指數及每單位風險下較高的報酬。 / This paper applied simulation optimization technique to search for the optimal asset allocation. Simulation optimization is the process of determining the values of the decision variables that optimize the values of the stochastic response variable generated from a simulation model. The decision variables in our case are the allocations of many kinds of assets. The response variable is a function of the expected wealth and the associated risk. The simulation optimization problem can be characterized as a stochastic search over a feasible exploration region. The method we applied is the evolution strategies and the optimization problem is formulated as a multi-period one with short-sale constraints. In order to verify the effectiveness of simulation optimization, we compared the resulting asset allocation with allocations obtaining using traditional portfolio insurance strategies including Buy-and-Hold, Constant Mix, Constant Proportion Portfolio Insurance, and Time-Invariant Portfolio Protection. We also used many indexes to evaluate performance of all kinds of strategies in this paper. Our empirical results indicated that using simulation optimization to search for the best asset allocation resulted in large volatilities, however, it significantly enhanced rate of return. As a whole, applying simulation optimization indeed gets the better performance, increases the final wealth, makes Sharpe Index large, and obtains the higher return under per unit risk.