TY - JOUR

T1 - Dynamic optimal mean-variance portfolio selection with stochastic volatility and stochastic interest rate

AU - Zhang, Yumo

N1 - Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2022

Y1 - 2022

N2 - This paper studies optimal portfolio selection problems in the presence of stochastic volatility and stochastic interest rate under the mean-variance criterion. The financial market consists of a risk-free asset (cash), a zero-coupon bond (roll-over bond), and a risky asset (stock). Specifically, we assume that the interest rate follows the Vasicek model, and the risky asset’s return rate not only depends on a Cox-Ingersoll-Ross (CIR) process but also has stochastic covariance with the interest rate, which embraces the family of the state-of-the-art 4/2 stochastic volatility models as an exceptional case. By adopting a backward stochastic differential equation (BSDE) approach and solving two related BSDEs, we derive, in closed form, the static optimal (time-inconsistent) strategy and optimal value function. Given the time inconsistency of the mean-variance criterion, a dynamic formulation of the problem is further investigated and the explicit expression for the dynamic optimal (time-consistent) strategy is derived. In addition, analytical solutions to some special cases of our model are provided. Finally, the impact of the model parameters on the efficient frontier and the behavior of the static and dynamic optimal asset allocations is illustrated with numerical examples.

AB - This paper studies optimal portfolio selection problems in the presence of stochastic volatility and stochastic interest rate under the mean-variance criterion. The financial market consists of a risk-free asset (cash), a zero-coupon bond (roll-over bond), and a risky asset (stock). Specifically, we assume that the interest rate follows the Vasicek model, and the risky asset’s return rate not only depends on a Cox-Ingersoll-Ross (CIR) process but also has stochastic covariance with the interest rate, which embraces the family of the state-of-the-art 4/2 stochastic volatility models as an exceptional case. By adopting a backward stochastic differential equation (BSDE) approach and solving two related BSDEs, we derive, in closed form, the static optimal (time-inconsistent) strategy and optimal value function. Given the time inconsistency of the mean-variance criterion, a dynamic formulation of the problem is further investigated and the explicit expression for the dynamic optimal (time-consistent) strategy is derived. In addition, analytical solutions to some special cases of our model are provided. Finally, the impact of the model parameters on the efficient frontier and the behavior of the static and dynamic optimal asset allocations is illustrated with numerical examples.

KW - Backward stochastic differential equation

KW - CIR process

KW - Dynamic optimality

KW - Mean-variance portfolio selection

KW - Vasicek interest rate

U2 - 10.1007/s10436-022-00414-x

DO - 10.1007/s10436-022-00414-x

M3 - Journal article

AN - SCOPUS:85137038891

VL - 18

SP - 511

EP - 544

JO - Annals of Finance

JF - Annals of Finance

SN - 1614-2446

ER -