Stochastic programs without duality gaps
For researchers in operations research and mathematical finance, this work offers theoretical guarantees for solving stochastic programs without duality gaps, though it is an incremental extension of existing no-arbitrage conditions.
The paper provides sufficient conditions for the existence of solutions and absence of duality gaps in dynamic stochastic optimization problems, using extended dynamic programming equations under relaxed conditions that generalize no-arbitrage conditions from mathematical finance.
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.