Robustness meets co-jumps: optimal consumption and portfolio choice with derivatives
研究了在股票和衍生品市场中，具有递归偏好的投资者如何应对模型不确定性和跳跃风险，得到最优消费与投资组合的近似解，并发现忽视模糊性会导致显著财富损失。
In this paper, we study a robust, dynamic, continuous-time optimal consumption and portfolio allocation problem for investors with recursive preferences who have access to both stock and derivatives markets. We assume the stock price process follows a stochastic volatility model, with instantaneous precision as the unique state variable, allowing for discontinuities in all the dynamics. We obtain a closed-form approximate solution up to a system of ODEs to the optimization problem for a non-unitary value of the elasticity of intertemporal substitution of consumption, being able to derive an exact solution as a particular case. Our theoretical findings show that the optimal policies are remarkably affected by the ambiguity-aversion parameters to diffusive and jump risks. A detailed numerical analysis confirms the effectiveness of our theoretical results on real data. Finally, we prove that investors who do not believe in ambiguity may suffer considerable wealth losses.