本研究探討一種無股息股票，其價格遵循狀態轉移的幾何布朗運動。在給定股票當前價格的情況下，賣出機制包括目標價格和止損限額。當價格達到目標價格或設定止損限額時，就會作出「賣出」決定。其主要目的是為了讓投資者受益。在他們的金融職業生涯中，投資者往往選擇弱勢個股，或者在錯誤的時間購買。因此，有必要盡快賣出這樣的股票以止損。實際上，目標價格通常約為 15% — 55% 的盈利水平，止損限額通常從 5% 至 20% 不等。然而，由於每個股票都有不同的特點，所以採用統一的規則來預定盈利和損失並不是一個好主意。此外，每個股票應以不同的清算規則來具體處理。
我們考察目標價格和止損限額的組合，從而確定那些必然提升預期收益函數值的組合。我們的目標是推導出這些價格限制。此外，我們確定預期目標週期和損益概率。在實踐中，衡量投資組合表現的常用標準是指定時段內的回報率百分比。然而，這樣的標準鼓勵在短期（τ0）內獲取小額利潤。顯然，這樣的標準並不適合個人投資者，尤其是那些無法持續監控其交易和額外交易成本的投資者。相比之下，折現因子降低了交易的頻率，因為它取代了時間作為持有週期的決定因素。折現收益函數在許多財務問題中很常見。
翻譯: 您學科領域的翻譯師翻譯您的原稿
In current study, we have a non-dividend single stock whose price observes a switching geometric Brownian motion. Given the current price of a stock the selling axiom 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. One often picks up the bad stock or the purchase made is at the wrong time. Therefore, it is necessary to sell it as soon as possible to stop loss. In practice, a target price is typically around a gain of 15%–55% and stop-loss limits generally vary from 5% to 20%. It is, however, not a good idea to adopt uniform profit taking. Each stock is different, it has own characterstics. Moreover, each stock should be treated differently with different liquidation rules.
In this study, we consider sets of target prices and stop-loss limits and choose target prices and stop-loss limits 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 for measuring the performance of portfolios is the percentage return per unit time. However, such a criterion leads to many transactions because of it encourages small profit-taking within short holding time τ0. Clearly, such a criteria is not suitable for retail investors, especially those who are unable to constantly monitor trading and additional transaction costs. A discount factor, in contrast, rules out very frequent transactions as it replaces time as the determinant of holding time. This discounted-reward function is natural in many financial problems.
雙語核對：雙語核對師依照原文檢查譯文是否正確，並修正錯誤
In current study, we have a non-dividend single stock whose price observesexhibits1 a regime-2switching geometric Brownian motion. Given the current price of a stock 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 career, Oneinvestors often picks up the badweak stocks or thea purchase made is at the wrong time. Therefore, it is necessary to sell it as soon as possible to stop losses3. In practice, a target price is typically around a gain of 15%–55% and stop-loss limits generally vary from 5% to 20%. It is, however, not a good idea to adopt uniform profit taking. Each stock is different, it has own characteristics4. Moreover, each stock should be treated differently with different liquidation rules.
In this study, we consider sets of target prices and stop-loss limits and choose target prices and stop-loss limitsdetermine those 5that 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 criteriacriterion for measuring the performance of portfolios is the percentage return per unit time. However, such a criterion leads to many transactions because of it encourages small profit-taking within short holding timeperiod6 (τ0). Clearly, such a criteria criterion is not suitable for retail investors, especially those who are unable to constantly monitor trading and additional transaction costs. A discount factor, in contrast, rules out very frequent transactions as it replaces time as the determinant of holding timeperiod. This discounted-reward function is natural common7 in many financial problems.
編修：英文母語編修師改善文章整體的流暢度與呈現方式
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 criteriainvestors frequently measure portfolio performance criterion for measuring theof 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.
完稿：翻譯完成品準時遞交給客戶
Given the current price of a stock, the selling principle 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 careers, investors often pick up weak stocks or purchase it at the wrong time. Therefore, in both the cases, it is often wise and necessary to sell such a stock as soon as possible to curtail losses. In practice, target prices are typically around a gain of 15%–55% and stop-loss limits generally vary from 5% to 20%. However, it is not a good idea to adopt uniform rules for booking profits and losses because each stock has its own characteristics that call for different liquidation rules.
In practice, investors frequently measure portfolio performance as the percentage return over given period. However, that criterion encourages taking small profits within a short holding period (τ0) and increases transaction costs. Hence, for those reasons, such a criterion may be unsuitable for retail investors, especially those who are unable to constantly monitor their portfolios. A discount factor, in contrast, reduces frequent transactions as it replaces time as the determinant of holding period. This discounted-reward function is commonly 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.
