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Malliavin method for optimal investment in financial markets with memory

100%

An Q. , Zhao G. , Zong G.

Open Mathematics

2016

tom 14

nr 1

286-299

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.

A logarithmic Sobolev inequality for one-dimensional multivalued stochastic differential equations

100%

Djehiche B. , Eddahbi M. , Ouknine Y.

Probability and Mathematical Statistics

2002

tom Vol. 22, Fasc. 1

13--18

We establish a logarithmic Sobolev inequality for a one-dimensional multivalued stochastic differential equation associated with the subdifferential of a convexlower semicontinuous function, using an explicit expression for the Malliavin derivative of the considered process. This result is given under some mild conditions on thecoefficients.