Abstract

We present a realization utility model with a stop-loss strategy, in which the investor will sell his position and leave the market instantly when the asset price drops to a certain preset level. The model gives the analytical solutions to the value function and the optimal liquidation point. We show that the stop-loss strategy will increase the value function and specifically the growth will be larger when the asset price is close to the stop-loss level, and smaller when the price is relatively high above from it. In addition, we show that the stop-loss strategy will decease the optimal liquidation point, which means it will induce the investor to voluntarily liquidate earlier at a lower take-profit level. Our results highlight the contribution of the stop-loss strategy to utility maximum, which could shed light on the value of this kind of strategies.

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