Markov Decision Processes with Average-Value-at-Risk criteria

We investigate the problem of minimizing the Average-Value-at-Risk (AV aRr) 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 conditions under which an optimal policy exists. We also give a time-consistent interpretation of the AV aRr . At the end we consider a numerical example which is a simple repeated casino game. It is used to discuss the influence of the risk aversion parameter r of the AV aRr-criterion

Some experiments on solving multistage stochastic mixed 0-1 programs with time stochastic dominance constraints

In this work we extend to the multistage case two recent risk averse measures for two-stage stochastic programs based on first- and second-order stochastic dominance constraints induced by mixed-integer linear recourse. Additionally, we consider Time Stochastic Dominance (TSD) along a given horizon. Given the dimensions of medium-sized problems augmented by the new variables and constraints required by those risk measures, it is unrealistic to solve the problem up to optimality by plain use of MIP solvers in a reasonable computing time, at least. Instead of it, decomposition algorithms of some type should be used. We present an extension of our Branch-and-Fix Coordination algorithm, so named BFC-TSD, where a special treatment is given to cross scenario group constraints that link variables from different scenario groups. A broad computational experience is presented by comparing the risk neutral approach and the tested risk averse strategies. The performance of the new version of the BFC algorithm versus the plain use of a state-of-the-artMIP solver is also reported

Compensation, Incentives and Risk-Taking in Principal-Agent Models

Two parties with distinct goals interact in a financial market: The risk-constrained principal provides some capital and employs the agent to invest and subsequently control the portfolio in his name. A performance-related wage schedule is agreed to compensate the agent for her actions. We investigate how risk can be transferred in this setup and what incentives are set by various contracts. In particular the high-water mark portfolio problem in discrete-time is solved