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We prove the existence of optimal strategies for agents with cumulativeprospect theory preferences who trade in a continuous-time illiquid market,transcending known results which pertained only to risk-averse utilitymaximizers. The arguments exploit an extension of Skorohod's representationtheorem for tight sequences of probability measures. This method is applicablein a number of similar optimization problems.

Skorohod's representation theorem and optimal strategies for markets with frictions