Dynamic optimal mean-variance portfolio selection with a 3/2 stochastic volatility
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Dynamic optimal mean-variance portfolio selection with a 3/2 stochastic volatility. / Zhang, Yumo.
In: Risks, Vol. 9, No. 4, 61, 2021.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Dynamic optimal mean-variance portfolio selection with a 3/2 stochastic volatility
AU - Zhang, Yumo
PY - 2021
Y1 - 2021
N2 - This paper considers a mean-variance portfolio selection problem when the stock price has a 3/2 stochastic volatility in a complete market. Specifically, we assume that the stock price and the volatility are perfectly negative correlated. By applying a backward stochastic differential equation (BSDE) approach, closed-form expressions for the statically optimal (time-inconsistent) strategy and the value function are derived. Due to time-inconsistency of mean variance criterion, a dynamic formulation of the problem is presented. We obtain the dynamically optimal (time-consistent) strategy explicitly, which is shown to keep the wealth process strictly below the target (expected terminal wealth) before the terminal time. Finally, we provide numerical studies to show the impact of main model parameters on the efficient frontier and illustrate the differences between the two optimal wealth processes.
AB - This paper considers a mean-variance portfolio selection problem when the stock price has a 3/2 stochastic volatility in a complete market. Specifically, we assume that the stock price and the volatility are perfectly negative correlated. By applying a backward stochastic differential equation (BSDE) approach, closed-form expressions for the statically optimal (time-inconsistent) strategy and the value function are derived. Due to time-inconsistency of mean variance criterion, a dynamic formulation of the problem is presented. We obtain the dynamically optimal (time-consistent) strategy explicitly, which is shown to keep the wealth process strictly below the target (expected terminal wealth) before the terminal time. Finally, we provide numerical studies to show the impact of main model parameters on the efficient frontier and illustrate the differences between the two optimal wealth processes.
KW - 3/2 stochastic volatility
KW - Backward stochastic differential equation
KW - Complete market
KW - Dynamic optimality
KW - Mean-variance portfolio selection
UR - http://www.scopus.com/inward/record.url?scp=85103896253&partnerID=8YFLogxK
U2 - 10.3390/risks9040061
DO - 10.3390/risks9040061
M3 - Journal article
AN - SCOPUS:85103896253
VL - 9
JO - Risks
JF - Risks
SN - 2227-9091
IS - 4
M1 - 61
ER -
ID: 261383048