Time-consistent investment policies in Markovian markets: A case of mean–variance analysis |
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Institution: | 1. Business School, Southern University of Science and Technology, Shenzhen, Guangdong, China;2. School of Data Science, City University of Hong Kong, China;3. College of Business, Shanghai University of Finance and Economics, China;4. Research Institute for Interdisciplinary Sciences, Shanghai University of Finance and Economics, China |
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Abstract: | 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. |
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Keywords: | Dynamic time consistency Mean–variance analysis Markovian markets Optimal investment policy Lagrange multiplier method |
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