Marcin Pitera (Jagelló Egyetem, Krakkó): Long-run risk-sensitive stochastic control: entropic formulation and MPE existence

Abstract: I will start with an outline of the long-run risk sensitive control problem in discrete time. In particular, I will discuss entropic problem formulation and show how this framework naturally emerges in various financial applications. Then, I will provide detailed comments on conditions implying existence of the bounded solution to the (non-controlled) Multiplicative Poisson Equation; this equation is closely linked to many risk-sensitive stochastic control problems. In particular, I will discuss which ergodic properties should be followed to ensure bounded solution existence and  how thIS interacts with reward function span-norm. I will also present multiple examples to help better understand MPE existence problem complexity.