Convex duality for Epstein–Zin stochastic differential utility
针对不完全市场中Epstein-Zin随机微分效用的消费投资问题，引入对偶问题并建立对偶关系，从而在较弱的假设下识别最优策略，并将对偶问题的最小化解解释为“最不利”的市场完备化。
Abstract This paper introduces a dual problem to study a continuous‐time consumption and investment problem with incomplete markets and Epstein–Zin stochastic differential utilities. Duality between the primal and dual problems is established. Consequently, the optimal strategy of this consumption and investment problem is identified without assuming several technical conditions on market models, utility specifications, and agent's admissible strategies. Meanwhile, the minimizer of the dual problem is identified as the utility gradient of the primal value and is economically interpreted as the “least favorable” completion of the market.