Ruin and investment in a Markovian environment.

Summary The purpose of this thesis is to model and optimize the investment strategies of an agent subject to a Markovian environment, and to a liquidity risk that arises when he can no longer face a cash outflow due to a lack of liquid assets. During this study, we will assume that his objective is to avoid bankruptcy. To do so, he has investment opportunities, allowing him to increase his future earnings in exchange for an immediate expense, thus risking a premature ruin since the investment is assumed to be illiquid: the goal of the work is to determine the conditions under which it is more judicious to run such a liquidity risk than to give up a permanent income.