Abstract : This PhD thesis is about the study of the long memory of the volatility of asset returns. In a first part, we bring an interpretation of long memory in terms of agents' behavior through a long memory volatility model whose parameters are linked with the bounded rational agents' heterogeneous behavior. We determine theoretically the necessary condition to get long memory. Then we calibrate our model from the daily realized volatility series of middle and large American capitalization stocks. Eventually, we observe the change in the agents' behavior between the period before the internet bubble burst and the one after. The second part is devoted to the consideration of long memory in portfolio management. We start by suggesting a stochastic volatility portfolio model in which the dynamics of the log-volatility is characterized by an Ornstein-Uhlenbeck process. We show that when the uncertainty of the future volatility level increases, it induces the revision of the consumption and investment plan. Then in a second model, we introduce a long memory component by the use of a fractional Brownian motion. As a consequence, it transposes the economic system from a Markovian framework to a non-Markovian one. So we provide a new resolution method based on Monte Carlo technique. Then we show the high importance to well model the volatility and warn the portfolio manager against the misspecification errors of the model.