Value-at-risk constrained portfolios in incomplete markets: a dynamic programming approach to Heston’s model
研究了在随机波动率导致的不完全市场中，对终端投资组合价值施加风险价值约束的期望效用最大化问题，通过动态规划推导最优策略，并发现低风险厌恶短期情景下约束与无约束配置有20%的相对差异。
Abstract We solve an expected utility-maximization problem with a Value-at-risk constraint on the terminal portfolio value in an incomplete financial market due to stochastic volatility. To derive the optimal investment strategy, we use the dynamic programming approach. We demonstrate that the value function in the constrained problem can be represented as the expected modified utility function of a vega-neutral financial derivative on the optimal terminal wealth in the unconstrained utility-maximization problem. Via the same financial derivative, the optimal wealth and the optimal investment strategy in the constrained problem are linked to the optimal wealth and the optimal investment strategy in the unconstrained problem. In numerical studies, we substantiate the impact of risk aversion levels and investment horizons on the optimal investment strategy. We observe a $$20\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>20</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> relative difference between the constrained and unconstrained allocations for average parameters in a low-risk-aversion short-horizon setting.