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

TL;DR

This paper extends Skorohod's representation theorem to prove the existence of optimal trading strategies for agents with prospect theory preferences in illiquid markets, broadening the scope beyond traditional utility maximization.

Contribution

It introduces a novel application of Skorohod's theorem to establish optimal strategies for prospect theory agents in continuous-time illiquid markets, surpassing prior utility-based results.

Findings

Existence of optimal strategies for prospect theory traders in illiquid markets.

Extension of Skorohod's representation theorem for probability measures.

Method applicable to various optimization problems.

Abstract

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