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Probability and Computational Finance Seminar
Sergio Pulido
Carnegie Mellon University
Title: Quadratic BSDEs arising from a price impact model with exponential utility

Abstract: We analyze a price impact model where a large investor wants to trade an illiquid asset with a market maker who quotes prices for this security. In our model, the market maker's preferences are modeled through an exponential utility function and the price impact of the trading strategy of the large investor is derived endogenously through an equilibrium mechanism. We establish a relationship between the equilibrium mechanism and a two-dimensional BSDE with quadratic growth. This allows us to show that an equilibrium exists under certain conditions on the final payoff of the traded asset, the risk aversion coefficient of the market maker and the trading strategy of the large investor. The relationship between the equilibrium mechanism and the two-dimensional quadratic BSDE also allows us to study stability and asymptotic behavior with respect to the parameters of the model. This is a joint project with Dmitry Kramkov.

Date: Monday, April 8, 2013
Time: 5:00 pm
Submitted by:  Dmitry Kramkov