Continuous-Time Mean-Variance Portfolio Selection with Inflation in an Incomplete Market

This paper concerns a continuous-time portfolio selection problem with inflation in an incomplete market. By using the approach of more general stochastic linear quadratic control technique (SLQ), we obtain the optimal strategy and efficient frontier to this problem. Furthermore, a numerical example is also provided.

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Xu, Y. and Wu, Z. (2014) Continuous-Time Mean-Variance Portfolio Selection with Inflation in an Incomplete Market. Journal of Financial Risk Management, 3, 19-28. doi: 10.4236/jfrm.2014.32003.

Conflicts of Interest

The authors declare no conflicts of interest.

 [1] Bensoussan, A., Keppo, J., & Sethi, S. P. (2009). Optimal Consumption and Portfolio Decisions with Partially Observed Real Prices. Mathematical Finance, 19, 215-236. http://dx.doi.org/10.1111/j.1467-9965.2009.00362.x [2] Bielecki, T. R., Jin, H., Pliska, S. R., & Zhou, X. Y. (2005). Continuous-Time Mean-Variance Portfolio Selection with Bankruptcy Prohibition. Mathematical Finance, 15, 213-244. http://dx.doi.org/10.1111/j.0960-1627.2005.00218.x [3] Brennan, M. J., & Xia, Y. (2002). Dynamic Asset Allocation under Inflation. The Journal of Finance, 57, 1201-1238.http://dx.doi.org/10.1111/1540-6261.00459 [4] Ji, S. (2010). Dual Method for Continuous-Time Markowitz’s Problems with Nonlinear Wealth Equations. Journal of Mathematical Analysis and Applications, 366, 90-100. http://dx.doi.org/10.1016/j.jmaa.2010.01.044 [5] Li, D., & Ng, W. L. (2000). Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation. Mathematical Finance, 10, 387-406. http://dx.doi.org/10.1111/1467-9965.00100 [6] Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7, 77-91. [7] Markowitz, H. (1959). Portfolio Selection: Efficient Diversification of Investments. New York: Wiley. [8] Merton, R. C. (1969). Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case. Review of Economics and Statistics, 51, 247-257. http://dx.doi.org/10.2307/1926560 [9] Merton, R. C. (1971). Optimum Consumption and Portfolio Rules in a Continuous-Time Model. Journal of Economic Theory, 3, 373-413. http://dx.doi.org/10.1016/0022-0531(71)90038-X [10] Xie, S., Li, Z., & Wang, S. (2008). Continuous-Time Portfolio Selection with Liability: Mean-Variance Model and Stochastic LQ Approach. Insurance: Mathematics and Economics, 42, 943-953. http://dx.doi.org/10.1016/j.insmatheco.2007.10.014 [11] Yong, J., & Zhou, X. Y. (1999). Stochastic Controls: Hamiltonian Systems and HJB Equations (Vol. 43). New York: Springer. http://dx.doi.org/10.1007/978-1-4612-1466-3 [12] Zhou, X. Y., & Li, D. (2000). Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework. Applied Mathematics and Optimization, 42, 19-33. http://dx.doi.org/10.1007/s002450010003