| Summary: | We solve a liquidation problem for an agent with prospect theory preferences who seeks to sell a portfolio of (divisible) claims on an underlying asset. Our methodology enables us to consider different formulations of prospect preferences in the literature, and various asset price processes. We find that these differences in specification are important - for instance, with piecewise power functions (but not piecewise exponentials) the agent may voluntarily liquidate at a loss relative to break-even. Further, we find that the likelihood of liquidating at a (small) gain is much higher than liquidating at a (large) loss, consistent with the disposition effect documented in empirical and experimental studies. The ability to partially liquidate also has significant consequences. The prospect agent liquidates the entire position at once, in contrast to behavior under standard concave preferences. If the position is divisible, under piecewise exponential functions, the agent no longer liquidates at the break-even level, and even if the asset is very poor, prefers to gamble on the possibility of liquidating at a gain. Finally, the piecewise power specification remains consistent with the disposition effect, albeit where the whole portfolio is sold at once.
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