Dynamic optimal mean-variance investment with mispricing in the family of 4/2 stochastic volatility models

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Dynamic optimal mean-variance investment with mispricing in the family of 4/2 stochastic volatility models. / Zhang, Yumo.

I: Mathematics, Bind 9, Nr. 18, 2293, 2021.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Zhang, Y 2021, 'Dynamic optimal mean-variance investment with mispricing in the family of 4/2 stochastic volatility models', Mathematics, bind 9, nr. 18, 2293. https://doi.org/10.3390/math9182293

APA

Zhang, Y. (2021). Dynamic optimal mean-variance investment with mispricing in the family of 4/2 stochastic volatility models. Mathematics, 9(18), [2293]. https://doi.org/10.3390/math9182293

Vancouver

Zhang Y. Dynamic optimal mean-variance investment with mispricing in the family of 4/2 stochastic volatility models. Mathematics. 2021;9(18). 2293. https://doi.org/10.3390/math9182293

Author

Zhang, Yumo. / Dynamic optimal mean-variance investment with mispricing in the family of 4/2 stochastic volatility models. I: Mathematics. 2021 ; Bind 9, Nr. 18.

Bibtex

@article{b86857d66f51436f92a3ecd0140e3712,
title = "Dynamic optimal mean-variance investment with mispricing in the family of 4/2 stochastic volatility models",
abstract = "This paper considers an optimal investment problem with mispricing in the family of 4/2 stochastic volatility models under mean–variance criterion. The financial market consists of a risk-free asset, a market index and a pair of mispriced stocks. By applying the linear–quadratic stochastic control theory and solving the corresponding Hamilton–Jacobi–Bellman equation, explicit expressions for the statically optimal (pre-commitment) strategy and the corresponding optimal value function are derived. Moreover, a necessary verification theorem was provided based on an assumption of the model parameters with the investment horizon. Due to the time-inconsistency under mean–variance criterion, we give a dynamic formulation of the problem and obtain the closed-form expression of the dynamically optimal (time-consistent) strategy. This strategy is shown to keep the wealth process strictly below the target (expected terminal wealth) before the terminal time. Results on the special case without mispricing are included. Finally, some numerical examples are given to illustrate the effects of model parameters on the efficient frontier and the difference between static and dynamic optimality.",
keywords = "4/2 stochastic volatility model, Dynamic optimality, Hamilton–Jacobi– Bellman equation, Mean–variance investment, Mispricing",
author = "Yumo Zhang",
year = "2021",
doi = "10.3390/math9182293",
language = "English",
volume = "9",
journal = "Mathematics",
issn = "2227-7390",
publisher = "MDPI AG",
number = "18",

}

RIS

TY - JOUR

T1 - Dynamic optimal mean-variance investment with mispricing in the family of 4/2 stochastic volatility models

AU - Zhang, Yumo

PY - 2021

Y1 - 2021

N2 - This paper considers an optimal investment problem with mispricing in the family of 4/2 stochastic volatility models under mean–variance criterion. The financial market consists of a risk-free asset, a market index and a pair of mispriced stocks. By applying the linear–quadratic stochastic control theory and solving the corresponding Hamilton–Jacobi–Bellman equation, explicit expressions for the statically optimal (pre-commitment) strategy and the corresponding optimal value function are derived. Moreover, a necessary verification theorem was provided based on an assumption of the model parameters with the investment horizon. Due to the time-inconsistency under mean–variance criterion, we give a dynamic formulation of the problem and obtain the closed-form expression of the dynamically optimal (time-consistent) strategy. This strategy is shown to keep the wealth process strictly below the target (expected terminal wealth) before the terminal time. Results on the special case without mispricing are included. Finally, some numerical examples are given to illustrate the effects of model parameters on the efficient frontier and the difference between static and dynamic optimality.

AB - This paper considers an optimal investment problem with mispricing in the family of 4/2 stochastic volatility models under mean–variance criterion. The financial market consists of a risk-free asset, a market index and a pair of mispriced stocks. By applying the linear–quadratic stochastic control theory and solving the corresponding Hamilton–Jacobi–Bellman equation, explicit expressions for the statically optimal (pre-commitment) strategy and the corresponding optimal value function are derived. Moreover, a necessary verification theorem was provided based on an assumption of the model parameters with the investment horizon. Due to the time-inconsistency under mean–variance criterion, we give a dynamic formulation of the problem and obtain the closed-form expression of the dynamically optimal (time-consistent) strategy. This strategy is shown to keep the wealth process strictly below the target (expected terminal wealth) before the terminal time. Results on the special case without mispricing are included. Finally, some numerical examples are given to illustrate the effects of model parameters on the efficient frontier and the difference between static and dynamic optimality.

KW - 4/2 stochastic volatility model

KW - Dynamic optimality

KW - Hamilton–Jacobi– Bellman equation

KW - Mean–variance investment

KW - Mispricing

UR - http://www.scopus.com/inward/record.url?scp=85115297133&partnerID=8YFLogxK

U2 - 10.3390/math9182293

DO - 10.3390/math9182293

M3 - Journal article

AN - SCOPUS:85115297133

VL - 9

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 18

M1 - 2293

ER -

ID: 284191263