Investment–consumption optimization with transaction cost and learning about return predictability
研究了在连续时间下，投资者面对可预测的资产收益率（含可观测和不可观测因子）时，如何通过动态学习和考虑交易成本来优化投资与消费决策，并给出了数值解法。
In this paper, we investigate an investment–consumption optimization problem in continuous-time settings, where the expected rate of return from a risky asset is predictable with an observable factor and an unobservable factor. Based on observable information, a decision-maker learns about the unobservable factor while making investment–consumption decisions. Both factors are supposed to follow a mean-reverting process. Also, we relax the assumption of perfect liquidity of the risky asset through incorporating proportional transaction costs incurred in trading the risky asset. In such way, a form of friction posing liquidity risk to the investor is examined. Dynamic programming principle coupled with an Hamilton–Jacobi–Bellman (HJB) equation are adopted to discuss the problem. Applying an asymptotic method with small transaction costs being taken as a perturbation parameter, we determine the frictional value function by solving the first and second corrector equations. For the numerical implementation of the proposed approach, a Monte-Carlo-simulation-based approximation algorithm is adopted to solve the second corrector equation. Finally, numerical examples and their economic interpretations are discussed.