Optimal Dynamic Asset Allocation and Optimal Insurance Design under Value at Risk Constraint

• Main Authors: Ching-ping Wang, 汪青萍
• Other Authors: David Shyu
• Format: Others
• Language: en_US
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/85058984630800728350

博士 === 國立中山大學 === 財務管理學系研究所 === 93 === This dissertation includes two topics. The first topic focuses on the problem of investor optimization of dynamic asset allocation to maximize expected utility under the value at risk (VaR) constraint. Different to previous researches, this study considers a common realistic case where the VaR horizon is equal to the whole investment horizon without a complete market constraint. Since the problem cannot be solved using the standard dynamic programming method or the martingale method, this study particularly provides an algorithm to solve this difficult problem. Similar to the mean-variance frontier suggested by Markowitz (1952), this study draws the frontiers of dynamic and static asset allocations under the VaR constraint. The analytical results clearly show that the dynamic asset allocations are more efficient than the static asset allocations. The second topic designs an optimal insurance policy form endogenously, assuming the objective of the insured is to maximize expected final wealth under the VaR constraint. The optimal insurance policy can be replicated using three options, including a long call option with a small strike price, a short call option with a large strike price, and a short cash-or-nothing call option. Moreover, expected wealth is increasing and concave in VaR and in significance level. Finally, Mean-VaR Frontiers are drawn, and reveal that the optimal insurance is more efficient than alternative insurance forms.