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研究生:陳姵吟
研究生(外文):Chen,Pei-Yin
論文名稱:OptimalAssetAllocationwithMinimumGuarantees
論文名稱(外文):附最低保證下之最適資產配置
指導教授:張士傑張士傑引用關係
指導教授(外文):Chang, Shi-Cheil
學位類別:碩士
校院名稱:國立政治大學
系所名稱:風險管理與保險研究所
學門:商業及管理學門
學類:風險管理學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:51
中文關鍵詞:minimum guaranteestochastic variationinterest rate riskmarket neutral valuationmutual fund
相關次數:
  • 被引用被引用:0
  • 點閱點閱:234
  • 評分評分:
  • 下載下載:23
  • 收藏至我的研究室書目清單書目收藏:2
本研究中,考慮連續時間下,附最低保證之長期最適投資策略;在利率模型中,為較能符合現實狀況,我們採用CIR模型;另外,在此策略中,我們將投資人之風險偏好加入模型中研究,最適化投資人到期時財富之效用函數,並用Cox & Huang之市場中立評價方法來解決數學模型問題。此篇研究顯示,最適之投資策略可以等價於某些共同基金之投資組合,這些共同基金能利用金融市場上之主要資產(market primary assets)來複製。
In this study, we consider a portfolio selection problem for long-term investors. Dynamic investment
strategy with the continuous-time framework incorporating the minimum guarantees are
constructed. Maximizing expected utility of the terminal wealth is employed by investors to trade
off profits in good future state against losses incurred in worse states. Follow the previous works
of Deelstra et al. (2003), we concentrate on the simplest case of a one-factor Cox-Ingersoll-Ross
(CIR) model in formulating the stochastic variation from the interest rate risks. Under the market
completeness assumption, the fund growth is modelled under the market neutral valuation and
the optimal rules are mapped into the static variational problem of Cox and Huang (1989). In
this study, we show that the optimal portfolio is equivalent to a certain mutual fund that can be
replicated by the market primary assets
Chapter 1 Introduction 1
Chapter 2 The Model 4
2.1 The Financial Market 4
2.2 The Optimization Program 10
Chapter 3 Transformation of The Initial Problem 13
Chapter 4 Explicit Solution in Iso-elastic Utility 14
Chapter 5 Solution of The Initial Problem 20
Chapter 6 Numerical Illustrations 25
6.1 The Investment Time Horizon 43
6.2 Minimum Interest Rate Guarantee 44
6.3 Risk Aversion Parameter 44
Chapter 7 Conclusion 45
References 45
Appendix A 47
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Cox, J. and Huang, C. F., 1989. Optimal consumption and portfolio policies when asset prices follow a diffusion process, Journal of Economic Theory 49, 33-83.
Cox, J. and Huang, C. F., 1991. A variational problem arising in financial economics. Journal of Mathematical Economics 20, 465-487.
Cox, J. C., Ingersoll, J. E. and Ross, S. A., 1985. A theory of the term structure of interest rates. Econometrica 53, 385-408.
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Karatzas, I., 1989. Optimization problems in the theory of continuous trading. Journal of Control and Optimization 27, 1221-1259.
Karatzas, I., and Shreve, S., 1991. Brownian Motion and Stochastic Calculus, Second ed. Springer-Verlag, Berlin.
Karatzas, I., Lehoczky, J. P. and Shreve, S., 1987. Optimal portfolio and consumption decision for a ''small investor'' on a finite horizon. SIAM. Journal on Control and Optimization 25, 1557-1586.
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Markowitz, H., 1959, Portfolio Selection: Efficient Diversification of Investment, John Wiley, New York.
Merton, R. C., 1971. Optimum consumption and portfolio rules in a continuous-time case. Journal of Economy Theory 3, 373-413.
Merton, R. C., 1969. Lifetime portfolio selection under uncertainty: The continuous-time case. Review of Economics and Statistics 51, 247--257.
Merton, R. C., 1973. An intertemporal capital asset pricing model. Econometrica 41 (5), 867--887.
Merton, R. C., 1992. Continuous Time Finance. Blackwell, Oxford.
Pliska, S., 1986. A stochastic calculus model of continuous trading: optimal portfolios. Mathematics of Operations Research 11, 371--382.
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