2015/04/08 by Teemu Penannen, Penannen, Teemu, Ari-Pekka Perkkiö +3
Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #math.OC #math.PR
paper · pdf · doi:10.48550/arxiv.1504.01903
15 pages
arxiv created 2015/04/08 · arxiv updated 2015/04/09
We establish the existence of minimizers in a rather general setting of dynamic stochastic optimization without assuming either convexity or coercivity of the objective function. We apply this to prove the existence of optimal portfolios for non-concave utility maximization problems in financial market models with frictions (such as illiquidity), a first result of its kind. The proofs are based on the dynamic programming principle whose validity is established under quite general assumptions.