# Malliavin method for optimal investment in financial markets with memory

Open Mathematics (2016)

• Volume: 14, Issue: 1, page 286-299
• ISSN: 2391-5455

top

## Abstract

top
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.

## How to cite

top

Qiguang An, Guoqing Zhao, and Gaofeng Zong. "Malliavin method for optimal investment in financial markets with memory." Open Mathematics 14.1 (2016): 286-299. <http://eudml.org/doc/277080>.

@article{QiguangAn2016,
abstract = {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.},
author = {Qiguang An, Guoqing Zhao, Gaofeng Zong},
journal = {Open Mathematics},
keywords = {Mean-field; Backward stochastic Volterra equations; Malliavin derivative; Maximum principle; mean-field backward stochastic Volterra equations; mean-field stochastic maximum principle; financial market; memory effects; optimal investment},
language = {eng},
number = {1},
pages = {286-299},
title = {Malliavin method for optimal investment in financial markets with memory},
url = {http://eudml.org/doc/277080},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Qiguang An
AU - Guoqing Zhao
AU - Gaofeng Zong
TI - Malliavin method for optimal investment in financial markets with memory
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 286
EP - 299
AB - 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.
LA - eng
KW - Mean-field; Backward stochastic Volterra equations; Malliavin derivative; Maximum principle; mean-field backward stochastic Volterra equations; mean-field stochastic maximum principle; financial market; memory effects; optimal investment
UR - http://eudml.org/doc/277080
ER -

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.