15 research outputs found
Stochastic programs without duality gaps
This paper studies dynamic stochastic optimization problems parametrized by a
random variable. Such problems arise in many applications in operations
research and mathematical finance. We give sufficient conditions for the
existence of solutions and the absence of a duality gap. Our proof uses
extended dynamic programming equations, whose validity is established under new
relaxed conditions that generalize certain no-arbitrage conditions from
mathematical finance
Nonconcave Robust Optimization with Discrete Strategies under Knightian Uncertainty
We study robust stochastic optimization problems in the quasi-sure setting in
discrete-time. The strategies in the multi-period-case are restricted to those
taking values in a discrete set. The optimization problems under consideration
are not concave. We provide conditions under which a maximizer exists. The
class of problems covered by our robust optimization problem includes optimal
stopping and semi-static trading under Knightian uncertainty.Comment: arXiv admin note: text overlap with arXiv:1610.0923