Risk-Averse Optimization 

Andrzej Ruszczynski 
Rutgers University 

We discuss stochastic optimization problems involving models 
of risk. At first we focus on problems involving convex 
measures of risk and we develop optimality and duality 
theory for these models. Then we pass to dynamic optimization 
problems with measures of risk and we present dynamic programming 
theory for such problems. In the next part we propose a new model 
involving stochastic dominance constraints with respect to random 
benchmarks. We  develop optimality and duality theory for these models. 
We  discuss connections of this model to the theories 
of expected utility and rank dependent expected utility. 
Finally we present an application to portfolio optimization.