Contribution to quantitative risk management in insurance.

Summary This document presents a synthesis of my work on mathematical problems applied to actuarial science. The theory of risk, also known as the theory of ruin, concerns in a general way the evaluation of probabilities of realizations of unfavorable events for insurance companies. Beyond these calculations of probabilities in a fixed model, branches of this theory are also interested in various optimization problems: allocation of reserves, dividend or taxation strategy (in the sense of taxation), investment in risky assets, reinsurance program.