Mind the cap!—constrained portfolio optimisation in Heston's stochastic volatility model
研究了赫斯顿随机波动率模型中面临凸约束的投资者的投资组合优化问题，发现约束的影响与布莱克-舒尔斯模型根本不同，但数值分析表明简单上限策略在大多数情况下损失很小，金融危机时除外。
We consider a portfolio optimisation problem for a utility-maximising investor who faces convex constraints on his portfolio allocation in Heston's stochastic volatility model. We apply existing duality methods to obtain a closed-form expression for the optimal portfolio allocation. In doing so, we observe that allocation constraints impact the optimal constrained portfolio allocation in a fundamentally different way in Heston's stochastic volatility model than in the Black Scholes model. In particular, the optimal constrained portfolio may be different from the naive ‘capped’ portfolio, which caps off the optimal unconstrained portfolio at the boundaries of the constraints. Despite this difference, we illustrate by way of a numerical analysis that in most realistic scenarios the capped portfolio leads to slim annual wealth equivalent losses compared to the optimal constrained portfolio. During a financial crisis, however, a capped solution might lead to compelling annual wealth equivalent losses.