Solving Constrained Consumption–Investment Problems by Simulation of Artificial Market Strategies
提出一种结合人工市场、闭式解和蒙特卡洛模拟的数值方法，求解存在约束和不完全市场的消费-投资问题，并给出财富等价损失的上界，对金融学者和实务者有参考价值。
Utility-maximizing consumption and investment strategies in closed form are unknown for realistic settings involving portfolio constraints, incomplete markets, and potentially a high number of state variables. Standard numerical methods are hard to implement in such cases. We propose a numerical procedure that combines the abstract idea of artificial, unconstrained complete markets, well-known closed-form solutions in affine or quadratic return models, straightforward Monte Carlo simulation, and a standard iterative optimization routine. Our method provides an upper bound on the wealth-equivalent loss compared to the unknown optimal strategy, and it facilitates our understanding of the economic forces at play by building on closed-form expressions for the strategies considered. We illustrate and test our method on the life-cycle problem of an individual who receives unspanned labor income and cannot borrow or short sell. The upper loss bound is small, and our method performs well in comparison with two existing methods. This paper was accepted by Wei Xiong, finance.