Optimization of Asset Allocation and Liquidation Time in Investment Decisions with VaR as a Risk Measure

Asset allocation and investment times are two correlated aspects of investments; however, most research on investment decisions focuses on asset allocation with investment times fixed. This study aims to provide methods to optimize both asset allocation and liquidation time. We use value at risk (VaR), the most widely used risk indicator in the financial industry, to measure the risk of an investment, and construct an investment decision model for risk-oriented investors, which is continuous-time VaR minimization. We adopt a statistical method to estimate VaR that avoids assumptions that are difficult to verify; the corresponding continuous-time VaR minimization model becomes unsolvable with conventional optimization methods. We first suggest an approach to solve the model by solving a sequence of discrete-time VaR minimization models. This approach leads to the optimal solution under some conditions but yields an approximation to the optimal in general. Solving more discrete-time VaR minimization models produces a better result but has an additional computational burden. To improve the efficiency of the optimality-seeking process, we propose a novel strategy to reduce computing load significantly. We examine the reliability of the strategy by conducting computation experiments with actual data from a stock market.