Some contributions to control and backward equations in finance.

Summary I was interested in solving some financial problems by stochastic control. We first considered a mixed problem of optimal investment and optimal sale. We studied the behavior of an investor who owns an indivisible asset that he wants to sell while continuously managing a portfolio of risky assets. Then, the study of first and second order backward stochastic equations with convex constraints was performed. In each case, we proved the existence of a minimal solution and a stochastic representation for this problem. Finally, we have studied a stochastic volatility model where the instantaneous volatility depends on the forward volatility curve. We propose an asymptotic development of the option price for small variations of the volatility.