1In current study, we have a non-dividend single stock whose price observes exhibits2 a uregime-3switching geometric Brownian motion. Given the current price of a stock,4 the selling axiomprinciple consists of target price and a stop-loss limit. A ‘sell’ decision is made when the price reaches either the target price or the set stop-loss limit. The main purpose is to benefit investors. During their financial careercareers, Oneinvestors often picks up the badweak stocks or thea purchase made is it at the wrong time. Therefore, in both the cases, it is often wise and necessary to sell itsuch a stock as soon as possible to stopcurtail losses5. In practice, a target price isprices are typically around a gain of 15%–55% and stop-loss limits generally vary from 5% to 20%. ItHowever, it is, however, not a good idea to adopt uniform profit taking. Each stock is different, it  rules for booking profits and losses because each stock has its own characteristics6. Moreover, each stock should be treated differently with7 that call for different liquidation rules.

In this study, we consider sets of target prices and stop-loss limits and choose target prices and stop-loss limits determine those8  that promise to enhance an expected reward function. We aim at deriving these price limits. In addition, we determine the expected target period and the probability of making and losing money. In practice, a frequent used criteria criterion for measuring theinvestors frequently measure portfolio performance of portfolios isas the percentage return per unit timeover given period. However, such athat criterion leads to many transactions because of it encourages small profit-taking small profits within a short holding timeperiod 9(τ0). and increases transaction costs.10 ClearlyHence, for those reasons, such a criteria criterion is not suitablemay be unsuitable 11for retail investors, especially those who are unable to constantly monitor trading and additional transaction costs, their portfolios. 12A discount factor, in contrast, rules out veryreduces frequent transactions as it replaces time as the determinant of holding timeperiod. This discounted-reward function is natural 13common incommonly applied to many financial problems.

This study examines a non-dividend single stock whose price exhibits a regime-switching geometric Brownian motion. We consider sets of stop-loss limits and target prices and determine those that promise to enhance an expected reward function. We aim to derive these limits as well as an expected holding period and probabilities of making and losing money.