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A speculative agent with Prospect Theory preference chooses the optimal time to purchase and then to sell an indivisible risky asset 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, the optimal strategy can be "buy and hold", "buy low sell high", "buy high sell higher" or "no trading". Behavioral preference and market friction interact in a subtle way which yields surprising implications on the agent's trading patterns. For example, increasing the market entry fee does not necessarily curb speculative trading, but instead it may induce a higher reference point under which the agent becomes more risk-seeking and in turn is more likely to trade. |
