We study the minimization of a spectral risk measure of the total discounted cost generated by a Markov Decision Process (MDP) over a finite or infinite planning horizon. The MDP is assumed to have Borel state and action spaces and the cost function may be unbounded above. The optimization...

We consider an insurance company whose risk reserve is given by a Brownian motion with drift and which is able to invest the money into a Black-Scholes financial market. As optimization criteria, we treat mean-variance problems, problems with other risk measures, exponential utility and the...