Applications of comonotonicity in finance.

Summary This thesis focuses on applications of comonotonicity in finance. In the first chapter, we use this notion to characterize the efficient random wealth, solutions of a budget constrained utility maximization problem, for markets with frictions. We derive a measure of inefficiency, not based on any particular utility. Applying these results, we study efficiency in the context of diffusion models. In the second chapter, we study efficiency in models with transaction costs. Considering multidimensional utility functions, we show that efficiency is then characterized by cyclical comonotonicity. Finally, in the last chapter, assuming that only the historical distribution of a risky asset at maturity, the value of the forward, and the price of a European call option are known, we bound the smile using a comonotonicity hypothesis.