Alex Schied, University of Waterloo

  pdf Presentation from Conference (1.80 MB)

Title: Superprocesses, singular control problems in finance, and path-dependent PDEs
Joint with Eyal Neuman and Alexander Kalinin

Abstract: We consider a class of stochastic control problems that are connected with the problem of finding adaptive mean-variance-optimal portfolio liquidation strategies in the Almgren-Chriss framework or in currency target zone models. We give closed-form solutions to these control problems in terms of the log-Laplace transforms of certain J-functionals of (catalytic) Dawson-Watanabe superprocesses. In the case of historical superprocesses, these log-Laplace transforms are mild solutions to a semilinear path-dependent PDE, and we show that they solve this path-dependent PDE also in the viscosity sense.