Stochastic control and numerical methods in mathematical finance.

Summary In the first part, we present a non-parametric method for estimating option price sensitivities using random perturbation of the parameter of interest, Monte Carlo simulations and kernel regression. For an irregular function, the estimator converges faster than finite difference estimators, which is numerically verified. The 2nd part proposes an algorithm for solving decoupled EDSPR systems with jumps. The discretization error in time is parametric. And the statistical error is controlled. We present numerical examples on coupled systems of semi-linear PDE. The 3rd part studies the behavior of a fund manager, maximizing the intertemporal utility of his consumption, under a drawdown constraint. We obtain in explicit form the optimal strategy in infinite horizon, and we characterize the value function in finite horizon as the unique viscosity solution of the corresponding HJB equation.