We investigate the problem of minimizing the Average-Value-at-Risk (AVaR τ ) of the discounted cost over a finite and an infinite horizon which is generated by a Markov Decision Process (MDP). We show that this problem can be reduced to an ordinary MDP with extended state space and give...

We consider a two-station network with two types of jobs: type 0 jobs require service at station 1 only and type 1 jobs require service both at station 1 and 2 in sequence. Each station has a single server. The problem is to schedule the server at station 1 between the two types of jobs in order...

In this paper we are interested in optimizing proportional reinsurance and investment policies in a multidimensional Lévy-driven insurance model. The criterion is that of maximizing exponential utility. Solving the classical Hamilton-Jacobi-Bellman equation yields that the optimal retention...

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...

We consider a discrete time version of the popular optimal dividend payout problem in risk theory. The novel aspect of our approach is that we allow for a risk averse insurer, i.e., instead of maximising the expected discounted dividends until ruin we maximise the expected utility of discounted...