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Stochastic Illiquidity: Optimal liquidation if resilience of price impact stochastic

Oberseminar Finanz- und Versicherungsmathematik


Stochastic Illiquidity: Optimal liquidation if resilience of price impact stochastic

Abstract

We solve explicitly a two-dimensional singular control problem of finite fuel type in infinite time horizon. The problem stems from the optimal liquidation of an asset position in a financial market with finite stochastic illiquidity. Price impact is multiplicative and transient with stochastic resilience. The optimal control is obtained as a diffusion process reflected at a non-constant free boundary. To solve the HJB variational inequality and prove optimality, we apply new results on the Laplace transforms of the inverse local times for diffusions reflected at elastic boundaries.
This talk is based on joint papers with Todor Bilarev and Peter Frentrup.