Stochastic control is concerned with making optimal decisions in the presence of uncertainty which is typically evolving with time. Its rich mathematical theory has found numerous applications, within mathematical finance, engineering, economics and other areas. Stochastic control combines probabilistic methods [P] with deep results and techniques from the analysis of non-linear partial differential equations [A] such as viscosity solutions. It raises challenges in the realm of numerical analysis [C] since explicit closed form solutions are rarely available and finding good approximations with computationally fast implementations is of paramount importance in the modern financial setting. A recent development has been the use of risk measures to quantify the risk arising in combining complex financial instruments. A key goal of future research will be to develop tools from stochastic control to allow the management of risk in a dynamic environment.

Researchers in this area: Hobson, Jacka, Kolokoltsov, Warren