Title
The One-Shot Problem: Solution to an open question of finite-fuel singular control with discretionary stopping
Abstract
In this talk, I will introduce a novel ‘one-shot’ solution technique resolving an open problem (Karatzas et al., Finite-fuel singular control with discretionary stopping, Stochastics 71:1-2 (2000)). Unexpectedly given the convexity of the latter problem, its waiting region is not necessarily connected. Along a typical sample path, the state process may even spend positive time in both of its connected components. The analysis reveals more generally that when fuel is limited, contrary to intuition, the solution without fuel is not necessarily indicative of the solution for small amounts of fuel. To resolve this, we recommend solving the ‘one-shot’ problem, which is one of optimal stopping, prior to employing the usual ‘guess and verify’ solution approach. This is joint work with John Moriarty.
Bio
Neofytos Rodosthenous is an Associate Professor in the Department of Mathematics of UCL. His research interests lie in stochastic control and optimisation, optimal stopping, free-boundary problems, stochastic games, mean-field games, sequential testing and change-point detections (disorder problems), with applications in financial mathematics, economics and operational research.