The main objective of the thesis is the study and the determination of an optimal navigation strategy, for a sailboat in an America's Cup race, by methods of stochastic optimization. Such methods are appropriate because the sailing team expects the wind to fluctuate over time in an unpredictable manner. Two preliminary models are designed as "proof of concept": they assume a shifty wind with two possible directions. The first model limits the potential actions of the yacht, by only allowing it either to continue on its current bearing or to tack. The second model allows additional bearings and aims at studying the concept of Wally. The third model is the main contribution of the thesis. It is based on a realistic wind model and a wide range of allowed yacht actions. It is designed for use during the first upwind leg of a regatta and can be used in real time, producing the trajectory recommendation which minimizes the expected time to the top mark that ends the leg. Other information is also provided, which quantifies the loss related to using non optimal actions or the advantage/disadvantage of other positions in the race field. Using Monte-Carlo simulations, we produce information about the probability of winning against the opponent, in terms of his current position. The last part of the thesis is dedicated to the implementation of an algorithm that stabilizes the output of a laser gun used on board the yacht during the races to determine the precise position of the opponent's yacht, which leads to estimates of direction and velocity. For this, we have developped a robust stabilization and automated filtering algorithm. We test this algorithm on real data.