Analysis of stochastic algorithms applied to finance.

Summary This thesis deals with the analysis of stochastic algorithms and their application in Finance. The first part presents a convergence result for stochastic algorithms where innovations verify averaging assumptions with a certain speed. We apply it to different types of innovations and illustrate it on examples mainly motivated by Finance. We then establish a "universal" speed of convergence result in the framework of equi-separated innovations and compare our results with those obtained in the i-framework. I. D. The second part is devoted to applications. We first present an optimal allocation problem applied to dark pools. The execution of the maximum desired quantity leads to the construction of a constrained stochastic algorithm studied in the innovation framework i. I. D. and averaging innovations. The next chapter presents a constrained stochastic optimization algorithm with projection to find the best placement distance in an order book by minimizing the execution cost of a given quantity. We then study the implementation and calibration of parameters in financial models by stochastic algorithm and illustrate these 2 techniques with examples of application on Black-Scholes, Merton and pseudo-CEV models. The last chapter deals with the application of stochastic algorithms in the framework of random urn models used in clinical trials. Using the ODE and DHS methods, we recover the convergence and speed results of Bai and Hu under weaker assumptions on the generating matrices.