Risk-Averse Control of Markov Systems

The speaker will focus on modeling risk in dynamical systems and discuss fundamental properties of dynamic measures of risk. Special attention will be paid to the local property and the property of time consistency. Then, the speaker will focus on risk-averse control of discrete-time Markov systems. The speaker will refine the concept of time consistency for such systems, introduce the class of Markovian risk measures, and derive their structure. This will allow the speaker to derive a risk-averse counterpart of dynamic programming equations. Then, the speaker will extend these ideas to partially-observable systems and continuous-time Markov chains, and derive the structure of risk measure and dynamic programming equations in these cases as well. In the last part of the talk, the speaker will discuss risk-averse control of diffusion processes and present a risk-averse counterpart of the Hamilton-Jacobi-Bellman equation. Finally, the speaker will review some solution methods for risk-averse control problems.