Time-consistent investment policies in Markovian markets: A case of mean-variance analysis

The optimal investment policy for a standard multi-period mean-variance model is not time-consistent because the variance operator is not separable in the sense of the dynamic programming principle. With a nested conditional expectation mapping, we develop an investment model with time consistency in Markovian markets. Furthermore, we examine the differences of the investment policies with a riskless asset from those without a riskless asset. Analytical solutions for time-consistent optimal investment policies and the resulting mean-variance efficient frontier are obtained. Finally, using numerical examples, we show that the optimal investment policy derived from our model is more efficient than that of the standard mean-variance model in which the trade-off is determined between the mean and variance of the terminal wealth.