The research group shall study optimal stopping and impulse control problems of Markov processes with long run multiplicative functionals.
We are planning to think on sufficient conditions for solutions of multiplicative Poisson equations and its applicability to change measure in the controlled problems.
One of the important problems is asymptotics of value functions with respect to risk parameter (which maybe positive or negative). The results will be applied to construct risk sensitive portfolios or generally feasible portfolios in the presence of a measure of risk.