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**Dynamic mean-variance asset allocation with stochastic interest rate and inflation rate.**
*(English)*
Zbl 1317.90248

Summary: This paper studies dynamic asset allocation with stochastic interest rates and inflation rates under the continuous-time mean-variance model in a more general market that may be incomplete. First, by the Lagrange method and the dynamic programming approach, we derive the associated Hamilton-Jacobi-Bellman equation and solve it explicitly. Then, closed form expressions for the efficient strategy and the efficient frontier are derived by applying the Lagrange dual theory. In addition, we state a necessary and sufficient condition under which the efficient frontier is a straight line in the standard deviation-mean plane, and some degenerate cases are discussed. Finally, empirical analysis based on real data from the Chinese market is presented to illustrate applications of the results obtained in this paper.

### MSC:

90C26 | Nonconvex programming, global optimization |

91G10 | Portfolio theory |

91G80 | Financial applications of other theories |

49N15 | Duality theory (optimization) |

### Keywords:

asset allocation; inflation; stochastic interest rate; dynamic mean-variance; Hamilton-Jacobi-Bellman equation
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\textit{H. Yao} et al., J. Ind. Manag. Optim. 12, No. 1, 187--209 (2016; Zbl 1317.90248)

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