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Existence and uniqueness results for multi-dimensional quadratic BSDEs arising from a price impact model with exponential utility

Banff International Research Station for Mathematical Innovation and Discovery

In this work we study multi-dimensional systems of quadratic BSDEs arising from a price impact model where an influential investor trades illiquid assets with a representative market maker with exponential preferences. The impact of the strategy of the investor on the prices of the illiquid assets is derived endogenously through an equilibrium mechanism. We show that a relationship exists between this equilibrium mechanism and a multi-dimensional system of quadratic BSDEs. We also specify conditions on the parameters of the model that guarantee that the system of BSDEs has a unique solution, which corresponds to a family of unique equilibrium prices for the illiquid assets. The proof relies on estimates that exploit the structure of the equilibrium problem. Finally, we provide examples of parameters for which the corresponding system of BSDEs in not well-posed. This is joint work with Dmitry Kramkov.

Mathematics; Game theory, economics, social and behavioral sciences; Probability theory and stochastic processes; Mathematical finance

video/mp4

Author affiliation: Swiss Finance Institute @ EPFL

2014-10-29

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/50931

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/