Malliavin method for optimal investment in financial markets with memory

• Autorzy: Qiguang An , Guoqing Zhao , Gaofeng Zong
• Języki publikacji: EN

Abstrakty

EN

We consider a financial market with memory effects in which wealth processes are driven by mean-field stochastic Volterra equations. In this financial market, the classical dynamic programming method can not be used to study the optimal investment problem, because the solution of mean-field stochastic Volterra equation is not a Markov process. In this paper, a new method through Malliavin calculus introduced in [1], can be used to obtain the optimal investment in a Volterra type financial market. We show a sufficient and necessary condition for the optimal investment in this financial market with memory by mean-field stochastic maximum principle.

Słowa kluczowe

EN

Mean-field; Backward stochastic Volterra equations; Malliavin derivative; Maximum principle

Kategorie tematyczne

• 60H20: Stochastic integral equations
• 35K60: Nonlinear initial value problems for linear parabolic equations
• 60H30: Applications of stochastic analysis (to PDE, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 286-299

Daty

wydano

2016-01-01

otrzymano

2015-09-08

zaakceptowano

2015-12-28

online

2016-05-19

Twórcy

autor

Qiguang An

• School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan,

autor

Guoqing Zhao

• School of Finance, Shandong University of Finance and Economics, Jinan,

autor

Gaofeng Zong

• School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250002,

Identyfikatory

DOI

10.1515/math-2016-0027