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.
@article{bwmeta1.element.doi-10_1515_math-2016-0027,
author = {Qiguang An and Guoqing Zhao and Gaofeng Zong},
title = {Malliavin method for optimal investment in financial markets with memory},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {286-299},
zbl = {1347.60081},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0027}
}
Qiguang An; Guoqing Zhao; Gaofeng Zong. Malliavin method for optimal investment in financial markets with memory. Open Mathematics, Tome 14 (2016) pp. 286-299. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0027/