论文标题
不完整市场中的价值风险限制投资组合：赫斯顿模型的动态编程方法
Value-at-Risk constrained portfolios in incomplete markets: a dynamic programming approach to Heston's model
论文作者
论文摘要
由于随机波动性，我们在不完整的金融市场中，对终端投资组合价值的价值约束解决了预期的公用事业最大化问题。为了获得最佳投资策略，我们使用动态编程方法。我们证明，受约束问题中的价值函数可以表示为在不受约束的效用最大化问题中，Vega中性金融衍生物的预期修改效用函数。通过相同的财务导数，最佳财富和受约束问题的最佳投资策略与无约束问题的最佳财富和最佳投资策略有关。在数值研究中，我们证实了风险规避水平和投资视野对最佳投资策略的影响。我们观察到在低风险 - 抑制短马设置中的平均参数的约束分配和未约束分配之间的相对差异为20％。
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% relative difference between the constrained and unconstrained allocations for average parameters in a low-risk-aversion short-horizon setting.
