Workshop MFG in Economics

Mathieu Rosenbaum (CEREMADE, Université Paris Dauphine - PSL) Titre : Volume, Volatility and market impact: a tale of three fractional brothers Abstract : Price volatility and order flow dynamics are two commonly used measures of the intensity of market fluctuations that are evidently closely related. However, on the one hand, the rough nature of the volatility is an undeniable stylized fact. On the other hand, smooth fractional Brownian motions have been proposed to capture the autocorrelation of the order flow, in contrast to the paradigm of rough volatility. We discuss how to resolve this apparent contradiction, providing new microstructural foundations for the joint dynamics of prices, volatility and volumes and making the connection with market impact. This is joint work with Johannes Muhle-Karbe, Youssef Ouazzabi Chahdi and  Grégoire Szymanski. Download slides

Speaker : Charles Bertucci (CEREMADE, Université Paris Dauphine - PSL) Title : The Equilibrium Price of Bubble Assets Abstract : Considering a simple economy, we derive a new Hamilton-Jacobi equation which is satisfied by the value of a ”bubble” asset. We then show, by providing a rigorous mathematical analysis of this equation, that a unique non-zero stable solution exists under certain assumptions. The economic interpretation of this result is that, if the bubble asset can produce more stable returns than fiat money, agents protect themselves from hazardous situations through the bubble asset, thus forming a bubble’s consensus value. Our mathematical analysis uses different ideas coming from the study of semi-linear elliptic equations. A joint work with Jean-Michel Lasry and Pierre-Louis Lions Download slides