Malliavin method for optimal investment in financial markets with memory-Reference-Cited by-同舟云学术

Malliavin method for optimal investment in financial markets with memory

Published:2016-01-01 Issue:1 Volume:14 Page:286-299
ISSN:2391-5455
Container-title:Open Mathematics
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Short-container-title:

Author:

An Qiguang¹,Zhao Guoqing²,Zong Gaofeng³

Affiliation:

1. 1School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, China

2. 2School of Finance, Shandong University of Finance and Economics, Jinan, China

3. 3School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250002, China

Abstract

AbstractWe 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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2016-0027/pdf

Reference19 articles.

1. Optimal Portfolio and Consumption Decisions for a Small Investor on a Finite Horizon KaratzasILehoczkyJPShreveSEOptimal Portfolio and Consumption Decisions for a Small Investor on a Finite HorizonSIAM Control Optim;Karatzas;SIAM J Control Optim,1987

2. Optimal Investment and Consumption with Transaction Costs ShreveSESonerHMOptimal Investment and Consumption with Transaction CostsAnn;Shreve;Appl Probab Appl Probab,1994

3. Optimal Consumption and Portfolio Policies When Asset Prices Follow a Diffusion Process CoxJHuangCFOptimal Consumption and Portfolio Policies When Asset Prices Follow a Diffusion ProcessJ;Cox;Econ Theory Econ Theory,1989

4. Necessary and Sufficient Conditions in the Problem of Optimal Investment in Incomplete Markets KramkovDSchachermayerWNecessary and Sufficient Conditions in the Problem of Optimal Investment in Incomplete MarketsAnn;Kramkov;Appl Probab Appl Probab,2003

5. The Condition on the Asymptotic Elasticity of Utility Functions and Optimal Investment in Incomplete Markets KramkovDSchachermayerWThe Condition on the Asymptotic Elasticity of Utility Functions and Optimal Investment in Incomplete MarketsAnn;Kramkov;Appl Probab Appl Probab,1999

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