Long memory, volatility and portfolio management.

Summary This thesis focuses on the study of the long memory of the volatility of stock returns. In the first part, we provide an interpretation of long memory in terms of agents' behavior thanks to a long memory volatility model whose parameters are related to the heterogeneous behaviors of agents that can be rational or boundedly rational. We determine theoretically the conditions necessary to obtain long memory. We then calibrate our model on the basis of daily realized volatility series of US mid and large cap stocks and observe the change in agents' behavior between the period preceding the bursting of the internet bubble and the one following it. The second part is devoted to the consideration of long memory in portfolio management. We start by proposing a model of portfolio choice with stochastic volatility in which the dynamics of log-volatility is characterized by an Ornstein-Uhlenbeck process. We show that increasing the level of uncertainty about future volatility induces a revision of the consumption and investment plan. Then, in a second model, we introduce the long memory thanks to the fractional Brownian motion. This has the consequence of transposing the economic system from a Markovian framework to a non-Markovian framework. We then provide a new resolution method based on the Monte Carlo technique. Then, we show the importance of modeling volatility correctly and warn the portfolio manager against model specification errors.