條件風險值限制下的最適投資組合

Abstract

此篇論文利用K.F.C. Yiu (2004)的方法觀察有風險衡量限制式下的投資組合最大化問題--以效用最大化來代表，利用Hamilton-Jacobi-Bellmen Equation及Lagrange multiplier來處理限制式，並用數值方法解HJB-equation及有限制式下的最佳資產配置投資組合的最佳化，分析其消費、效用、資產總值。 此外本文也觀察在不同的資產報酬分配下CVaR限制式與VaR限制式下的最適化投資組合的不同，討論其結果是否與直覺相同，並更能合適的評斷投資的市場風險。我們發現有風險衡量限制式下，在風險資產的投資會減少，且在具極端值的資產報酬分配下，CVaR較能有效控管風險。

This paper looks at the optimal portfolio when a conditional value-at-risk dynamic constraint is imposed and analyses the consumption, utility and asset value in the portfolio. The optimal portfolio problem is formulated as a constrained maximization of expected utility. This follows the method used in K.F.C. Yiu (2004). The dynamic programming technique is applied to derive the HJB equation, the method of Lagrange multiplier is used to tackle the constraint and numerical method is proposed to solve the HJB equation and the optimal constrained portfolio allocation. The paper also looks the difference of portfolio under different asset loss distributions and different risk measure constraints, compares the result to intuitions and hopes to find a way to measure market risk adequately. We find that investments in risky assets are reduced by the imposed constraint, and the CVaR constraint is more powerful under an asset loss distribution with an extreme event.