This paper investigates a dynamic trading problem with transaction cost and uncertain exit time in a general Markov market, where the mean vector and covariance matrix of returns depend on the states of the stochastic market, and the market state is regime switching in a time varying state set. Following the framework proposed by Gârleanu and Pedersen (2013), the investor maximizes his or her multi-period mean–variance utility, net of quadratic transaction costs capturing the linear price impact where trades lead to temporary linear changes in prices. The explicit expression for the optimal strategy is derived by using matrix theory technique and dynamic programming approach. Finally, numerical examples are provided to study the effects of transition cost and exit probability on the wealth process, the trading strategy, turnover rate and the total transaction cost.

本文研究了一般马尔可夫市场中具有交易成本和退出时间不确定的动态交易问题，其中收益的均值向量和协方差矩阵取决于随机市场的状态，市场状态是随时间变化的状态切换放。按照 Gârleanu 和 Pedersen (2013) 提出的框架，投资者最大化他或她的多期平均方差效用，扣除二次交易成本，在交易导致价格暂时线性变化的情况下捕捉线性价格影响。采用矩阵理论技术和动态规划方法推导出最优策略的显式表达式。最后通过数值例子研究了转型成本和退出概率对财富过程、交易策略、