We consider a general class of optimization problems in financial markets with incomplete information and transaction costs. Under a no-arbitrage condition strictly weaker than the existence of a martingale measure, and when asset prices are quasi-left-continuous processes, we show the existence of optimal strategies. Applications include maximization of expected utility, minimization of coherent risk measures and hedging of contingent claims.
"Optimal investment with transaction costs and without semimartingales." Ann. Appl. Probab. 12 (4) 1227 - 1246, November 2002. https://doi.org/10.1214/aoap/1037125861