近年來在許多國家皆能觀察到房價節節攀升的現象，其中不以自住為目的，而是以賺取房屋出租租金及資本利得的投資客，是影響房價高漲的重要推手之一。不同於相關文獻多數致力於探討不動產的最適持有期間，本研究則是針對投資者以濾嘴法則決定不動產的賣出時點，也就是在投資者設有停利點的設定之下，試圖推導不動產最適停利準則的閉合形式解，藉以了解不動產的最佳賣出時機。本文假設房價的隨機過程符合幾何布朗運動，並利用碰觸到停利點的機率密度函數推導出停利點的閉合形式解，此解為使不動產淨現值最大的停利點，亦即投資者的最適停利準則。接著本文就目前相關研究中，缺乏分析投資者特性影響不動產持有期間的角度切入，將投資者具有不同效用函數(CRRA以及展望理論之效用函數)納入考量，討論在不同效用函數下，投資者風險趨避程度對於最適停利準則的影響。另外，本研究也針對投資客的貸款程度，以及是否設定停損準則，探討其最適停利點的變化。最後，利用靜態比較分析討論不動產市場波動程度、無風險利率等參數的變動，對最適停利點的影響，並期待本研究能為各國政府未來打房政策的制定提供值得參考的資訊。

Housing price is observed skyrocketing during recent years in many countries. One of the key causes of this rapid increase in housing price is the investor who invests in real estate for the purpose of earning rents and capital gains rather than for residence purpose. Unlike most related researches focus on finding the optimal real estate holding period, our study aims at deriving closed-form solution for optimal stop-gain rule under the condition that investors sell properties based on filter rules. We first assume that housing price follows a geometric Brownian motion process and then apply the probability density function of first hitting time to stop-gain point for deriving the optimal stop-gain rule which maximizes the net present value of the real estate. Next, this paper studies the impact of investor characteristics on optimal selling time which is still limited in literature. Two kinds of utility functions including constant relative risk aversion (CRRA) utility function and prospect theory utility function are considered, and how the risk aversion level influence optimal stop-gain rule is analyzed under these two utility functions. Furthermore, this study also discusses the impact of different stop-loss point and loan-to-value (LTV) ratio on optimal stop-gain rule. Finally, static comparative analysis shows how the optimal selling time varies according to value changes in parameters such as housing market volatility and risk-free rate. We expect this study to provide valuable information for assisting governments in the future development of policies on curbing housing prices.

Chapter 1: Introduction 1
Chapter 2: Literature Review 2
Chapter 3: Methodology 4
3.1 Stop-gain rule 4
3.2 First hitting time probability density function and the optimal stop-gain
rule 6
3.3 CRRA and prospect theory utility function 8
3.3.1 CRRA utility function 8
3.3.2 Prospect theory utility function 8
3.4 Optimal stop-gain rule under CRRA and prospect theory utility function 9
3.4.1 Expected net present value of cash flows 9
3.4.2 Simulation of optimal stop-gain rule 10
Chapter 4: Comparative Statics Analysis 10
4.1 Variation in risk-free rate r 11
4.1.1 Effect on optimal stop-gain rule 11
4.1.2 Effect on and mean of U(V_(t_i ) (u)) 13
Variation in volatility of housing market σ 15
4.2.1 Effect on optimal stop-gain rule 15
4.2.2 Effect on and mean of U(V_(t_i ) (u)) 16
4.3 Variation in trend of real estate return μ 18
4.3.1 Effect on optimal stop-gain rule 18
4.3.2 Effect on and mean of U(V_(t_i ) (u)) 19
4.4 Variation in investor’s risk aversion γ 21
Chapter 5: Conclusion 23
Appendix A 25
Appendix B 27
Reference 28

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