Speculative Trading, Prospect Theory and Transaction Costs

Abstract

A speculative agent with Prospect Theory preference chooses the optimal time to purchase and then to sell an indivisible risky asset as to maximize the expected utility of the round-trip profit net of transaction costs. The optimization problem is formulated as a sequential optimal stopping problem and we provide a complete characterization of the solution. Depending on the preference and market parameters as well as the initial price of the asset, the optimal strategy can be "buy and hold", "buy low sell high", "buy high sell higher" or "no trading". Transaction costs do not necessarily curb speculative trading. For example, while a large proportional transaction cost on sale can unambiguously suppress trading participation, introducing a fixed market entry fee will indeed encourage trading when the asset price level is high.