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題名 Optimal Asset Allocation with Minimum Guarantees
附最低保證下之最適資產配置
作者 陳姵吟
Chen,Pei-Yin
貢獻者 張士傑
Chang, Shi-Cheil
陳姵吟
Chen,Pei-Yin
關鍵詞 minimum guarantee
stochastic variation
interest rate risk
market neutral valuation
mutual fund
日期 2003
上傳時間 18-Sep-2009 19:24:01 (UTC+8)
摘要 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
參考文獻 Bajeux-Besnainou, 2003. Dynamic asset allocation for stocks, bonds, and cash. Journal of Business 76, 263-287.
Barberis, N., 2000. Investing for the long run when returns are predictable. Journal of Finance 55 (1), 225-264.
Basak, S., 1995. A general equilibrium model of portfolio insurance, Review of Financial Study 8, 1059-1090.
Breeden, D., 1979. An intertemporal asset pricing model with stochastic consumption and investment opportunities. Journal of Financial Economics 7 (3), 265--296.
Chan, K. C., Karolyi, G. A. and Longstaff, F. S., Sanders, A.B.,1992. The volatility of short-term interest rates: an empirical comparison of alternative models of the term structure of interest rates. Journal of Finance 47, 1209-1227.
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.
Deelstra, G., Grasselli, M. and Koehl, P. F., 2000. Optimal investment strategies in a CIR framework. Journal of Applied Probability 37, 936-946.
Deelstra, G., Grasselli, M. and Koehl, P. F., 2003. Optimal investment strategies in the presence of a minimum guarantee. Insurance:Mathematics and Economics 33, 189-207.
Dempster, M. A. H., Evstigneev, I. V. and Schenk-Hoppe, K.R., 2003. Exponential growth of fixed-mix strategies in stationary asset markets, Finance and Stochastics, 7, 263-276.
Devolder, P., Princep, M. B. and Fabian, I. D., 2003. Stochastic optimal control of annuity contracts, Insurance: Mathematics and Economics 33, 227-238.
Duffie, J. D. and Huang, C. F., 1985. Implementing Arrow-Debreu equilibria by continuous trading of few long-lived securities, Econometrica, 53 1337-1356.
Grossman, S., and Z. Zhou, 1996. Equilibrium analysis of portfolio insurance, Journal of Finance 51, 1379-1403.
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.
Long, J. B., 1990. The numeraire portfolio. Journal of Financial Economics 26, 29--69.
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.
描述 碩士
國立政治大學
風險管理與保險研究所
91358019
92
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0091358019
資料類型 thesis
dc.contributor.advisor 張士傑zh_TW
dc.contributor.advisor Chang, Shi-Cheilen_US
dc.contributor.author (Authors) 陳姵吟zh_TW
dc.contributor.author (Authors) Chen,Pei-Yinen_US
dc.creator (作者) 陳姵吟zh_TW
dc.creator (作者) Chen,Pei-Yinen_US
dc.date (日期) 2003en_US
dc.date.accessioned 18-Sep-2009 19:24:01 (UTC+8)-
dc.date.available 18-Sep-2009 19:24:01 (UTC+8)-
dc.date.issued (上傳時間) 18-Sep-2009 19:24:01 (UTC+8)-
dc.identifier (Other Identifiers) G0091358019en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/36732-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 風險管理與保險研究所zh_TW
dc.description (描述) 91358019zh_TW
dc.description (描述) 92zh_TW
dc.description.abstract (摘要) 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。zh_TW
dc.description.abstract (摘要) 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
en_US
dc.description.tableofcontents 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
zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0091358019en_US
dc.subject (關鍵詞) minimum guaranteeen_US
dc.subject (關鍵詞) stochastic variationen_US
dc.subject (關鍵詞) interest rate risken_US
dc.subject (關鍵詞) market neutral valuationen_US
dc.subject (關鍵詞) mutual funden_US
dc.title (題名) Optimal Asset Allocation with Minimum Guaranteeszh_TW
dc.title (題名) 附最低保證下之最適資產配置zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Bajeux-Besnainou, 2003. Dynamic asset allocation for stocks, bonds, and cash. Journal of Business 76, 263-287.zh_TW
dc.relation.reference (參考文獻) Barberis, N., 2000. Investing for the long run when returns are predictable. Journal of Finance 55 (1), 225-264.zh_TW
dc.relation.reference (參考文獻) Basak, S., 1995. A general equilibrium model of portfolio insurance, Review of Financial Study 8, 1059-1090.zh_TW
dc.relation.reference (參考文獻) Breeden, D., 1979. An intertemporal asset pricing model with stochastic consumption and investment opportunities. Journal of Financial Economics 7 (3), 265--296.zh_TW
dc.relation.reference (參考文獻) Chan, K. C., Karolyi, G. A. and Longstaff, F. S., Sanders, A.B.,1992. The volatility of short-term interest rates: an empirical comparison of alternative models of the term structure of interest rates. Journal of Finance 47, 1209-1227.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) Cox, J. and Huang, C. F., 1991. A variational problem arising in financial economics. Journal of Mathematical Economics 20, 465-487.zh_TW
dc.relation.reference (參考文獻) Cox, J. C., Ingersoll, J. E. and Ross, S. A., 1985. A theory of the term structure of interest rates. Econometrica 53, 385-408.zh_TW
dc.relation.reference (參考文獻) Deelstra, G., Grasselli, M. and Koehl, P. F., 2000. Optimal investment strategies in a CIR framework. Journal of Applied Probability 37, 936-946.zh_TW
dc.relation.reference (參考文獻) Deelstra, G., Grasselli, M. and Koehl, P. F., 2003. Optimal investment strategies in the presence of a minimum guarantee. Insurance:Mathematics and Economics 33, 189-207.zh_TW
dc.relation.reference (參考文獻) Dempster, M. A. H., Evstigneev, I. V. and Schenk-Hoppe, K.R., 2003. Exponential growth of fixed-mix strategies in stationary asset markets, Finance and Stochastics, 7, 263-276.zh_TW
dc.relation.reference (參考文獻) Devolder, P., Princep, M. B. and Fabian, I. D., 2003. Stochastic optimal control of annuity contracts, Insurance: Mathematics and Economics 33, 227-238.zh_TW
dc.relation.reference (參考文獻) Duffie, J. D. and Huang, C. F., 1985. Implementing Arrow-Debreu equilibria by continuous trading of few long-lived securities, Econometrica, 53 1337-1356.zh_TW
dc.relation.reference (參考文獻) Grossman, S., and Z. Zhou, 1996. Equilibrium analysis of portfolio insurance, Journal of Finance 51, 1379-1403.zh_TW
dc.relation.reference (參考文獻) Karatzas, I., 1989. Optimization problems in the theory of continuous trading. Journal of Control and Optimization 27, 1221-1259.zh_TW
dc.relation.reference (參考文獻) Karatzas, I., and Shreve, S., 1991. Brownian Motion and Stochastic Calculus, Second ed. Springer-Verlag, Berlin.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) Long, J. B., 1990. The numeraire portfolio. Journal of Financial Economics 26, 29--69.zh_TW
dc.relation.reference (參考文獻) Markowitz, H., 1959, Portfolio Selection: Efficient Diversification of Investment, John Wiley, New York.zh_TW
dc.relation.reference (參考文獻) Merton, R. C., 1971. Optimum consumption and portfolio rules in a continuous-time case. Journal of Economy Theory 3, 373-413.zh_TW
dc.relation.reference (參考文獻) Merton, R. C., 1969. Lifetime portfolio selection under uncertainty: The continuous-time case. Review of Economics and Statistics 51, 247--257.zh_TW
dc.relation.reference (參考文獻) Merton, R. C., 1973. An intertemporal capital asset pricing model. Econometrica 41 (5), 867--887.zh_TW
dc.relation.reference (參考文獻) Merton, R. C., 1992. Continuous Time Finance. Blackwell, Oxford.zh_TW
dc.relation.reference (參考文獻) Pliska, S., 1986. A stochastic calculus model of continuous trading: optimal portfolios. Mathematics of Operations Research 11, 371--382.zh_TW