Malliavin calculus for two-parameter processes
Malliavin method for optimal investment in financial markets with memory
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....
Markov operators defined by Volterra type integrals with advanced argument
Martingales on noncompact manifolds : maximal inequalities and prescribed limits
Mild solutions of quantum stochastic differential equations.
Minimal supersolutions of BSDEs with lower semicontinuous generators
We study minimal supersolutions of backward stochastic differential equations. We show the existence and uniqueness of the minimal supersolution, if the generator is jointly lower semicontinuous, bounded from below by an affine function of the control variable, and satisfies a specific normalization property. Semimartingale convergence is used to establish the main result.