Three essays on the theory of continuous-time financial markets.

Summary This thesis consists of three essays on the theory of incomplete financial markets in continuous time. In the first chapter, we study the valuation of measurable contingent assets with respect to an information structure richer than that generated by the price of the traded assets. We show that the absence of arbitrage opportunity (AOA) gives rise to a price interval for and characterize hedge prices using two auxiliary stochastic control problems. Since the bounds of the interval are associated with near-safe hedging, each price within it induces a risk of loss and, hence, the choice of a price can only be made with respect to a risk norm representing the agent's preferences. In the second chapter, we immerse the valuation problem in the optimal portfolio choice problem and study the notion of utility prices. In particular, we show that such prices exist, that they are compatible with the AOA and that they have many interesting properties. In the case of default-prone assets, and more generally in the case of credit derivatives, we solve the problem explicitly and present many numerical examples. The third chapter deals with the optimal portfolio choice in a delegated management model. The manager chooses not only the composition of the fund but also a consumption plan in order to maximize his utility. The investor also seeks to maximize his utility but only has access to the financial market through the fund and pays a commission for this. We formulate the problem of simultaneous utility maximization for both agents in the context of a stochastic game whose solution is obtained explicitly. The solution is closely related to the microeconomic treatment of monopoly situations. In particular, in equilibrium, the value functions do not depend on either the manager's utility function or the commission rate.