We consider an optimal execution problem in which the agent holds either shares on an asset which they are restricted from trading, or an option with such an asset as the underlier. The agent is, however, allowed to trade in another correlated asset. We account for the possibility of price impact, both permanent and temporary, due to the agent's trades. We also include a new feature which is the impact that the agent's trades in a single asset will have on the price of the other asset, deemed cross price impact. When the agent holds shares of an untraded asset we solve in closed form for the optimal trading strategy. When the claim held by the agent has payoff which is non-linear in the untraded asset, we solve in closed form for an approximation of the optimal trading strategy which applies when cross price impact and risk-aversion are small.
*Texto informado pelo autor.
Ryan Donnelly is a Lecturer in Financial Mathematics at Kings College London. Previously he was a postdoctoral researcher at EPFL (2014-17) and the Universtiy of Washington (2017-19). He's a PhD from the University of Toronto (2014).