Stability and analytic expansions of local solutions of systems of quadratic BSDEs with applications to a price impact model
We obtain stability estimates and derive analytic expansions for local solutions of multi-dimensional quadratic BSDEs. We apply these results to a financial model where the prices of risky assets are quoted by a representative dealer in such a way that it is optimal to meet an exogenous demand. We show that the prices are stable under the demand process and derive their analyticexpansions for small risk aversion coefficients of the dealer. We briefly discuss related results that naturally arise when studying the replication and optimal investment problems under this model of price impact. This is joint work with Dmitry Kramkov.