Effective Approximation Methods for Constrained Utility Maximization with Drift Uncertainty
针对带有闭凸控制约束和部分信息的效用最大化问题，提出一种有效近似方法，通过分离原理和对偶关系将问题转化为误差最小化随机控制问题，并给出价值函数的紧上下界及近似值。
Abstract In this paper, we propose a novel and effective approximation method for finding the value function for general utility maximization with closed convex control constraints and partial information. Using the separation principle and the weak duality relation, we transform the stochastic maximum principle of the fully observable dual control problem into an equivalent error minimization stochastic control problem and find the tight lower and upper bounds of the value function and its approximate value. Numerical examples show the goodness and usefulness of the proposed method.