臺灣博碩士論文加值系統

本研究建構了一個效用極大化的模型，並推導出影響最適LTV 比率的因素，模
型參數數據化模擬的結果得到五個結論。最適LTV 比率與勞動收入、初始金融資
產和房價成長呈正向相關，與起始房價呈負向相關，最適LTV 比率與實質資產報
酬率之間的相關性並不確定，其取決於屋主的財富。這個模型建議中低收入的家庭
應該獲得較低的最適LTV 比率，避免非住宅的效用過度下降，而高收入的家庭可
以獲得更高的最適LTV 比率，用來投資以獲得更多的最終財富效用。

This study builds a model with utility maximization and derived the factors that affect the optimal LTV ratio. The results of parameters quantification results in five conclude for the model simulation. The optimal LTV ratio has a positive relationship with labor income, initial financial assets, and housing price growth, a negative relationship with initial housing prices. The correlation between the optimal LTV ratio and the real return on assets is uncertain, which depend on the wealth of the household. The model suggests that the households with low-medium-income should obtain a lower optimal LTV ratio in order to avoid the excessive decline in non-housing consumption utility. The households with high-income may obtain a higher optimal LTV ratio for the purpose of investment that increases the terminal wealth utility.

Content

中文摘要 i
Abstract ii
誌 謝 iii
Content iv
Figure content vi
Table content vii
1 Introduction 1
1.1 Research background and motivation 1
1.2 Research purpose 4
2. Literature review 6
2.1 Utility maximization 6
2.2 LTV ratio and optimal LTV ratio 8
3. The model 12
3.1 Utility function 12
3.2 Time parameter 14
3.3 Labor income and housing parameter 15
3.4 Mortgage 16
3.5 Model summary 17
3.6 Model solution 18
4. Model parameter numerical simulation 22
4.1 Quantify parameters 22
4.1.1 Time factor 22
4.1.2 Growth rate 24
4.1.3 Initial and baseline value 24
4.1.4 Tax and other 25
4.2 Model numerical simulation 25
4.2.1 Housing price growth 26
4.2.2 Real return on assets rate 43
4.3 Empirical data examine 57
5. Conclusion 59
References 62
Appendix A. Low initial financial assets (0.5 million) and housing price growth 67
Appendix B. medium initial financial assets (1 million) and housing price growth 70
Appendix C. high initial financial assets (1.5 million) and housing price growth 73
Appendix D. low initial financial assets (1 million) and real return on assets rate 76
Appendix E. medium initial financial assets (2 million) and real return on assets rate 79
Appendix F. high initial financial assets (3 million) and real return on assets rate 82
Appendix G: Proofs 85

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