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題名 薪資所得與通貨膨脹不確定性於確定提撥退休金計畫
Hedging Labor Income Inflation Uncertainties through Capital Market in Defined Contribution Pension Schemes
作者 黃雅文
Hwang Ya-wen
貢獻者 張士傑
黃雅文
Hwang Ya-wen
關鍵詞 確定提撥
薪資的不確定性
通貨膨脹
隨機控制
動態規劃
defined contribution
salary uncertainty
inflation
stochastic control
dynamic programming
日期 2004
上傳時間 2009-09-18
摘要 本文於確定提撥退休金制度下，探討基金經理人如何決定最適資產策略規避薪資所得及通貨膨脹之不確定風險，求得期末財富效用期望值極大化。本研究首先擴展Battocchio與Menoncin (2004)所建構之資產模型，我們不僅探討來自市場之風險，同時考量薪資所得、通貨膨脹與費用率之不確定性，研究其對最適資產配置行為的影響，建構隨機控制模型，以動態規劃方法求解Hamiltonian方程式，研究結果顯示，我們可利用五項共同基金分離定理來描述投資人之最適投資決策：短期市場基金、狀態變數避險基金、薪資所得避險基金、通貨膨脹避險基金與現金部位。數值結果顯示，股票持有部位中通貨膨脹避險基金佔有最大的成份，債券持有部位中通貨膨脹避險基金與狀態變數避險基金佔有最大的成份。
關鍵字：確定提撥、薪資的不確定性、通貨膨脹、隨機控制、動態規劃
In this study, we investigate the portfolio selection problem in order to hedge the labor income and inflation uncertainties for defined contribution (DC) pension schemes. First, we extend the previous work of Battocchio and Menoncin (2004) that allowed the state variables (i.e., the risks from the financial market) and a set of stochastic processes to describe the inflation, labor income and expense uncertainties. A five-fund separation theorem is derived to characterize the optimal investment strategy for DC pension plans to hedge the labor income and the inflation risks. Second, by solving the Hamiltonian equation in the three-asset framework, we show that the optimal portfolio consists of five components: the myopic market portfolio, the hedge portfolio for the state variables, the hedge portfolio for the inflation risk, the hedge portfolio for the labor income uncertainty and the riskless asset. Then we explicitly solve the optimal portfolio problem. Finally, the numerical results indicate that the inflation hedge portfolio comprises the overwhelming proportion of stock holdings in the optimal portfolios. In addition, the inflation hedge portfolio and the state variable hedge portfolio constitute the overwhelming proportions of bond holdings.
Keywords: defined contribution; salary uncertainty; inflation; stochastic control; dynamic programming.
參考文獻 References
[1] Battocchio, P., Menoncin, F., 2004. Optimal portfolio strategies with sto-
chastic wage income and in‡ation: the case of a de…ned contribution pen-
sion plan. Working Paper CeRP, No. 19-02. Torino, Italy.
[2] Battocchio, P., Menoncin, F., 2004. Optimal Pension management in a
stochastic framework. Insurance: Mathematics and Economics 34, 79-95.
[3] Black, D., Cairns, A. J. G., Dowd, K., 2000. Optimal dynamic asset allo-
cation for de…ned-contribution plans. The Pension Institute, London, Dis-
cussion Paper PI 2003.
[4] Boulier, J. F., Huang, S. J., Taillard, G., 2001. Optimal management under
stochastic interest. Insurance: Mathematics and Economics 28, 173-189.
[5] Boyle, P. and Yang, H., 1997. Asset allocation with time variation in ex-
pected returns, Insurance: Mathematics and Economics, 21, 201-218.
[6] Brennan, M. J., Schwartz, E. S., Lagnado R., 1997. Strategic asset alloca-
tion, Journal of Economics, Dynamics and Control, 21, 1377-1403.
[7] Brennan, M. J., Schwartz E. S., 1982. An equilibrium model of bond pric-
ing and a test of market e¢ ciency, Journal of Financial and Quantitative
Analysis, 17, 301-329.
[8] Brennan, M. J. and Schwartz, E. S. Schwartz, 1998. The use of treasury
bill futures in strategic asset allocation programs. In Worldwide Asset and
Liability Modeling. (J.M.Mulvey andW.T. Ziemba, Eds.) Cambridge, Eng-
land: Cambridge University Press, 205-230.
[9] Brimson, G. P., Hood, L. R., & Beelower, G. L. (1986). Determinants of
portfolio performance. Financial Analysts Journal, 42, 39-44.
[10] Brimson, G. P., et.al., (1990). Determinants of portfolio performance II:
An update. Financial Analysts Journal, 47,40-48.
[11] Cairns, A. J. G., 2000. Some notes on the dynamics and optimal control
of stochastic pension fund models in continuous time, ASTIN Bulletin, 30,
19-55.
[12] Campbell, J. Y., Cocco, J., Gomes, F., Maenhout P. 2001. Investing re-
tirement wealth: a life cycle model, in Risk Aspects of Investment-Based
Social Security Reform, Edited by Campbell, J. Y., Feldstein, M., editors,
Chicago University Press, Chicago.
[13] Campbell, J. Y., Viceira L. M., 1999. Consumption and portfolio decisions
when expected returns are time varying, Quarterly Journal of Economics,
114, 433-495.
1
[14] Campbell, J. Y., Viceira L. M., 2001. Who should buy long-term bonds,
American Economic Review, 91, 99-127.
[15] Campbell, J. Y., Viceira L. M., 2002. Strategic asset allocation - portfolio
choice for long-term investors, Oxford University Press.
[16] Chang, S. C., 1999. Optimal pension funding through dynamic simulations:
the case of Taiwan public employees retirement system, Insurance: Math-
ematics and Economics, 24, 187-199.
[17] Chang, S. C., 2000. Realistic pension funding: a stochastic approach, Jour-
nal of Actuarial Practice, 8, 5-42.
[18] Chang, S. C., Tsai, C. H., Tien, C. J., Tu, C. Y. , 2002. Dynamic funding
and investment strategy for de…ned bene…t pension schemes: model incor-
porating asset-liability matching criterion, Journal of Actuarial Practice,
10, 131-155.
[19] Chang, S. C., Tzeng, L. Y., Miao, C. Y., 2003. Pension funding incorporat-
ing downside risks, Insurance: Mathematics and Economics, 32, 217-228.
[20] Cox, J. C., Huang, C. F., 1991. A variational problem arising in …nancial
economics. Journal of Mathematical Economics 20, 465-487.
[21] Deelstra, G., Grasselli, M., Koehl, P. F., 2003. Optimal investment strate-
gies in the presence of a minimum guarantee. Insurance: Mathematics and
Economics 33, 189-207.
[22] Du¢ e, D., 1996. Dynamic Asset Pricing Theory. Princeton University
Press, Princeton.
[23] Fisher I., 1930. The Theory of Interest. New York: A. M. Kelly.
[24] Haberman, S., Sung, J. H., 1994. Dynamic approaches to pension funding,
Insurance: Mathematics and Economics, 15, 151-162.
[25] Haberman, S., Vigna, E., 2001. Optimal investment strategy for de…ned
contribution pension schemes. Insurance: Mathematics and Economics 28,
233-262.
[26] Heaton, J., Lucas, D. 1997. Market frictions, savings behavior and portfolio
choice, Macroeconomic Dynamics, 1, 76-101.
[27] Huang, H., Imrohoroglu, S., Sargent, T. J. 1997. Two computations to fund
social security, Macroeconomic Dynamics,1(1), 7-44.
[28] Imrohoroglu, A., Imrohoroglu, S., Joines, D. 1995. A life cycle analysis of
social security, Economic Theory, 6, 83-114.
[29] Imrohoroglu, A., Imrohoroglu, S., Joines, D. 1999a. A dynamic stochastic
general equilibrium analysis of social security, in Kehoe, T., Prescott, E.,
eds., The Discipline of Applied General Equilibrium, Springer-Verlag.
2
[30] Josa-Fombellida, R., Rinc-Zapatero, J. P., 2001. Minimization of risks in
pension funding by means of contributions and portfolio selection, Insur-
ance: Mathematics and Economics, 29, 35-45.
[31] Karatzas, I., Lehoczky, J. P., Sethi, S. P., Shreve, S. E., 1986. Explicit
solutions of a 30 general consumption investment problem, Mathematics of
Operations Research, 11, 261-294.
[32] Koo, H. K. 1998. Consumption and portfolio selection with labor income:
a continuous time approach, Mathematical Finance, 8, 49-65.
[33] Karatzas, I., Shreve, S. 1991. Brownian Motion and Stochastic Calculus.
Springer, New York.
[34] Kim, T., Omberg, E., 1996. Dynamic nonmyopic portfolio behavior, Review
of Financial Studies 9, 141-161.
[35] Lioui, A., Poncet, P., 2001. On optimal portfolio choice under stochastic
interest rates. Journal of Economic Dynamic and Control 25, 1841-1865.
[36] Madsen, J. B. 2002. The share market boom and the recent disin‡ation
in the OECD countries: the tax-e¤ects, the in‡ation-illusion, and the risk-
aversion hypotheses reconsidered. Quarterly Review of Economics and Fi-
nance, 42, 115-141.
[37] Markowitz, H. M., 1952. Portfolio selection. Journal of Finance 7(1), 77-91.
[38] Markus, R., William, T., Z., 2004. Intertemporal surplus management.
Journal of Economic Dynamics and Control 28, 975-990.
[39] Menoncin, F., 2002. Optimal portfolio and background risk: an exact and
an approximated solution, Insurance: Mathematics and Economics, 31,
249-265.
[40] Merton, R. C. 1969. Lifetime portfolio selection under uncertainty: The
continuous time case. Review of Economics and Statistics 51, 247-257.
[41] Merton, R. C. 1971. Optimum consumption and portfolio rules in a con-
tinuous time model. Journal of Economic Theory 3, 373-413.
[42] Merton, R. C. 1990. Continuous-time Finance. Blackwell, Cambridge, MA.
[43] Modigliani, F., John, R. A. 1979. In‡ation, rational valuation and the mar-
ket. Financial Analysts Journal, 24-44.
[44] O’Brien, T., 1986. A stochastic-dynamic approach to pension funding, In-
surance: Mathematics and Economics, 5, 141-146.
[45] O’Brien, T., 1987. A two-parameter family of pension contribution func-
tions and stochastic optimization, Insurance: Mathematics and Economics,
6, 129-134.
3
[46] Ritter, J. R., Warr, R. S. 2002. The decline of in‡ation and the bull market
of 1982 to 1999. Journal of Financial and Quantitative Economics, 37, 29-
61.
[47] Runggaldier, W. J., 1998. Concept and methods for discrete and continuous
time control under uncertainty, Insurance: Mathematics and Economics,
22, 25-39.
[48] Rutkowski. M., 1999. Self-…nancing trading strategies for sliding, rolling-
horizon, and consol bonds. Mathematical Finance 9, no. 4, 361-365.
[49] Samuelson, P., 1969. Lifetime portfolio selection by dynamic stochastic
programming, Review of Economics and Statistics, 51, 239-246.
[50] Schäl, M., 1998. On piecewise deterministic Markov control processes: con-
trol of jumps and of risk processes in insurance, Insurance: Mathematics
and Economics, 22, 75-91.
[51] Sharpe, W. F., 1991. Capital asset prices with and without negative hold-
ings, Journal of Finance, 64, 489-509.
[52] Sorensen, C., 1999. Dynamic asset allocation and …xed income manage-
ment, Journal of Financial and Quantitative Analysis, 34, 513-531.
[53] Vasicek, O. E. 1997. An equilibrium characterization of the term structure.
Journal of Financial Economics 5, 177-188.
[54] Viceira L. M., 2001. Optimal portfolio choice for long-horizon investors
with non-tradable labor income, Journal of Finance, 56, 433-470.
[55] Wachter, J. A., 2002. Portfolio and consumption decisions under mean-
reverting returns: an exact solution for complete markets, Journal of Fi-
nancial and Quantitative Analysis, 37, 63-91.
4
描述 碩士
國立政治大學
風險管理與保險研究所
92358007
93
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0923580071
資料類型 thesis
dc.contributor.advisor 張士傑zh_TW
dc.contributor.author (Authors) 黃雅文zh_TW
dc.contributor.author (Authors) Hwang Ya-wenen_US
dc.creator (作者) 黃雅文zh_TW
dc.creator (作者) Hwang Ya-wenen_US
dc.date (日期) 2004en_US
dc.date.accessioned 2009-09-18-
dc.date.available 2009-09-18-
dc.date.issued (上傳時間) 2009-09-18-
dc.identifier (Other Identifiers) G0923580071en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/34162-
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) 92358007zh_TW
dc.description (描述) 93zh_TW
dc.description.abstract (摘要) 本文於確定提撥退休金制度下，探討基金經理人如何決定最適資產策略規避薪資所得及通貨膨脹之不確定風險，求得期末財富效用期望值極大化。本研究首先擴展Battocchio與Menoncin (2004)所建構之資產模型，我們不僅探討來自市場之風險，同時考量薪資所得、通貨膨脹與費用率之不確定性，研究其對最適資產配置行為的影響，建構隨機控制模型，以動態規劃方法求解Hamiltonian方程式，研究結果顯示，我們可利用五項共同基金分離定理來描述投資人之最適投資決策：短期市場基金、狀態變數避險基金、薪資所得避險基金、通貨膨脹避險基金與現金部位。數值結果顯示，股票持有部位中通貨膨脹避險基金佔有最大的成份，債券持有部位中通貨膨脹避險基金與狀態變數避險基金佔有最大的成份。
關鍵字：確定提撥、薪資的不確定性、通貨膨脹、隨機控制、動態規劃		zh_TW
dc.description.abstract (摘要) In this study, we investigate the portfolio selection problem in order to hedge the labor income and inflation uncertainties for defined contribution (DC) pension schemes. First, we extend the previous work of Battocchio and Menoncin (2004) that allowed the state variables (i.e., the risks from the financial market) and a set of stochastic processes to describe the inflation, labor income and expense uncertainties. A five-fund separation theorem is derived to characterize the optimal investment strategy for DC pension plans to hedge the labor income and the inflation risks. Second, by solving the Hamiltonian equation in the three-asset framework, we show that the optimal portfolio consists of five components: the myopic market portfolio, the hedge portfolio for the state variables, the hedge portfolio for the inflation risk, the hedge portfolio for the labor income uncertainty and the riskless asset. Then we explicitly solve the optimal portfolio problem. Finally, the numerical results indicate that the inflation hedge portfolio comprises the overwhelming proportion of stock holdings in the optimal portfolios. In addition, the inflation hedge portfolio and the state variable hedge portfolio constitute the overwhelming proportions of bond holdings.
Keywords: defined contribution; salary uncertainty; inflation; stochastic control; dynamic programming.		en_US
dc.description.tableofcontents Contents
1. Introduction………………………………………………………………………1
1.1 The retirement system………………………………………………………3
1.2 The asset allocation problem………………………………………………..4
1.3 The development of the multi-period problems…………………………….4
1.4 Background risks……………………………………………………………4
1.5 The main approach in this article……………………………………………7
2. Proposed Model…………………………………………………………………...9
2.1 Financial market………..…………………………………………………....9
2.2 Labor income process…….…………….…………………………………..12
2.3 Inflation rate……………………..…….………………………..……….…12
2.4 The fund wealth…………………………………………………………….13
3. Asset Allocation Problem………………………………………………………..14
3.1 The stochastic optimal control……………………………………………..14
3.2 An exact solution…………………………………………………………..16
3.3 Second component of the optimal portfolio……………………………….17
4. Numerical Illustration…………………………………………………………...19
5. Conclusion………………………………………………………………………21
6. Appendix A ……………….…………………………………………………..23
7. Appendix B……………………………………………………………………...24
Reference……………………………………………………………………………25		zh_TW
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0923580071en_US
dc.subject (關鍵詞) 確定提撥zh_TW
dc.subject (關鍵詞) 薪資的不確定性zh_TW
dc.subject (關鍵詞) 通貨膨脹zh_TW
dc.subject (關鍵詞) 隨機控制zh_TW
dc.subject (關鍵詞) 動態規劃zh_TW
dc.subject (關鍵詞) defined contributionen_US
dc.subject (關鍵詞) salary uncertaintyen_US
dc.subject (關鍵詞) inflationen_US
dc.subject (關鍵詞) stochastic controlen_US
dc.subject (關鍵詞) dynamic programmingen_US
dc.title (題名) 薪資所得與通貨膨脹不確定性於確定提撥退休金計畫zh_TW
dc.title (題名) Hedging Labor Income Inflation Uncertainties through Capital Market in Defined Contribution Pension Schemesen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Referenceszh_TW
dc.relation.reference (參考文獻) [1] Battocchio, P., Menoncin, F., 2004. Optimal portfolio strategies with sto-zh_TW
dc.relation.reference (參考文獻) chastic wage income and in‡ation: the case of a de…ned contribution pen-zh_TW
dc.relation.reference (參考文獻) sion plan. Working Paper CeRP, No. 19-02. Torino, Italy.zh_TW
dc.relation.reference (參考文獻) [2] Battocchio, P., Menoncin, F., 2004. Optimal Pension management in azh_TW
dc.relation.reference (參考文獻) stochastic framework. Insurance: Mathematics and Economics 34, 79-95.zh_TW
dc.relation.reference (參考文獻) [3] Black, D., Cairns, A. J. G., Dowd, K., 2000. Optimal dynamic asset allo-zh_TW
dc.relation.reference (參考文獻) cation for de…ned-contribution plans. The Pension Institute, London, Dis-zh_TW
dc.relation.reference (參考文獻) cussion Paper PI 2003.zh_TW
dc.relation.reference (參考文獻) [4] Boulier, J. F., Huang, S. J., Taillard, G., 2001. Optimal management underzh_TW
dc.relation.reference (參考文獻) stochastic interest. Insurance: Mathematics and Economics 28, 173-189.zh_TW
dc.relation.reference (參考文獻) [5] Boyle, P. and Yang, H., 1997. Asset allocation with time variation in ex-zh_TW
dc.relation.reference (參考文獻) pected returns, Insurance: Mathematics and Economics, 21, 201-218.zh_TW
dc.relation.reference (參考文獻) [6] Brennan, M. J., Schwartz, E. S., Lagnado R., 1997. Strategic asset alloca-zh_TW
dc.relation.reference (參考文獻) tion, Journal of Economics, Dynamics and Control, 21, 1377-1403.zh_TW
dc.relation.reference (參考文獻) [7] Brennan, M. J., Schwartz E. S., 1982. An equilibrium model of bond pric-zh_TW
dc.relation.reference (參考文獻) ing and a test of market e¢ ciency, Journal of Financial and Quantitativezh_TW
dc.relation.reference (參考文獻) Analysis, 17, 301-329.zh_TW
dc.relation.reference (參考文獻) [8] Brennan, M. J. and Schwartz, E. S. Schwartz, 1998. The use of treasuryzh_TW
dc.relation.reference (參考文獻) bill futures in strategic asset allocation programs. In Worldwide Asset andzh_TW
dc.relation.reference (參考文獻) Liability Modeling. (J.M.Mulvey andW.T. Ziemba, Eds.) Cambridge, Eng-zh_TW
dc.relation.reference (參考文獻) land: Cambridge University Press, 205-230.zh_TW
dc.relation.reference (參考文獻) [9] Brimson, G. P., Hood, L. R., & Beelower, G. L. (1986). Determinants ofzh_TW
dc.relation.reference (參考文獻) portfolio performance. Financial Analysts Journal, 42, 39-44.zh_TW
dc.relation.reference (參考文獻) [10] Brimson, G. P., et.al., (1990). Determinants of portfolio performance II:zh_TW
dc.relation.reference (參考文獻) An update. Financial Analysts Journal, 47,40-48.zh_TW
dc.relation.reference (參考文獻) [11] Cairns, A. J. G., 2000. Some notes on the dynamics and optimal controlzh_TW
dc.relation.reference (參考文獻) of stochastic pension fund models in continuous time, ASTIN Bulletin, 30,zh_TW
dc.relation.reference (參考文獻) 19-55.zh_TW
dc.relation.reference (參考文獻) [12] Campbell, J. Y., Cocco, J., Gomes, F., Maenhout P. 2001. Investing re-zh_TW
dc.relation.reference (參考文獻) tirement wealth: a life cycle model, in Risk Aspects of Investment-Basedzh_TW
dc.relation.reference (參考文獻) Social Security Reform, Edited by Campbell, J. Y., Feldstein, M., editors,zh_TW
dc.relation.reference (參考文獻) Chicago University Press, Chicago.zh_TW
dc.relation.reference (參考文獻) [13] Campbell, J. Y., Viceira L. M., 1999. Consumption and portfolio decisionszh_TW
dc.relation.reference (參考文獻) when expected returns are time varying, Quarterly Journal of Economics,zh_TW
dc.relation.reference (參考文獻) 114, 433-495.zh_TW
dc.relation.reference (參考文獻) 1zh_TW
dc.relation.reference (參考文獻) [14] Campbell, J. Y., Viceira L. M., 2001. Who should buy long-term bonds,zh_TW
dc.relation.reference (參考文獻) American Economic Review, 91, 99-127.zh_TW
dc.relation.reference (參考文獻) [15] Campbell, J. Y., Viceira L. M., 2002. Strategic asset allocation - portfoliozh_TW
dc.relation.reference (參考文獻) choice for long-term investors, Oxford University Press.zh_TW
dc.relation.reference (參考文獻) [16] Chang, S. C., 1999. Optimal pension funding through dynamic simulations:zh_TW
dc.relation.reference (參考文獻) the case of Taiwan public employees retirement system, Insurance: Math-zh_TW
dc.relation.reference (參考文獻) ematics and Economics, 24, 187-199.zh_TW
dc.relation.reference (參考文獻) [17] Chang, S. C., 2000. Realistic pension funding: a stochastic approach, Jour-zh_TW
dc.relation.reference (參考文獻) nal of Actuarial Practice, 8, 5-42.zh_TW
dc.relation.reference (參考文獻) [18] Chang, S. C., Tsai, C. H., Tien, C. J., Tu, C. Y. , 2002. Dynamic fundingzh_TW
dc.relation.reference (參考文獻) and investment strategy for de…ned bene…t pension schemes: model incor-zh_TW
dc.relation.reference (參考文獻) porating asset-liability matching criterion, Journal of Actuarial Practice,zh_TW
dc.relation.reference (參考文獻) 10, 131-155.zh_TW
dc.relation.reference (參考文獻) [19] Chang, S. C., Tzeng, L. Y., Miao, C. Y., 2003. Pension funding incorporat-zh_TW
dc.relation.reference (參考文獻) ing downside risks, Insurance: Mathematics and Economics, 32, 217-228.zh_TW
dc.relation.reference (參考文獻) [20] Cox, J. C., Huang, C. F., 1991. A variational problem arising in …nancialzh_TW
dc.relation.reference (參考文獻) economics. Journal of Mathematical Economics 20, 465-487.zh_TW
dc.relation.reference (參考文獻) [21] Deelstra, G., Grasselli, M., Koehl, P. F., 2003. Optimal investment strate-zh_TW
dc.relation.reference (參考文獻) gies in the presence of a minimum guarantee. Insurance: Mathematics andzh_TW
dc.relation.reference (參考文獻) Economics 33, 189-207.zh_TW
dc.relation.reference (參考文獻) [22] Du¢ e, D., 1996. Dynamic Asset Pricing Theory. Princeton Universityzh_TW
dc.relation.reference (參考文獻) Press, Princeton.zh_TW
dc.relation.reference (參考文獻) [23] Fisher I., 1930. The Theory of Interest. New York: A. M. Kelly.zh_TW
dc.relation.reference (參考文獻) [24] Haberman, S., Sung, J. H., 1994. Dynamic approaches to pension funding,zh_TW
dc.relation.reference (參考文獻) Insurance: Mathematics and Economics, 15, 151-162.zh_TW
dc.relation.reference (參考文獻) [25] Haberman, S., Vigna, E., 2001. Optimal investment strategy for de…nedzh_TW
dc.relation.reference (參考文獻) contribution pension schemes. Insurance: Mathematics and Economics 28,zh_TW
dc.relation.reference (參考文獻) 233-262.zh_TW
dc.relation.reference (參考文獻) [26] Heaton, J., Lucas, D. 1997. Market frictions, savings behavior and portfoliozh_TW
dc.relation.reference (參考文獻) choice, Macroeconomic Dynamics, 1, 76-101.zh_TW
dc.relation.reference (參考文獻) [27] Huang, H., Imrohoroglu, S., Sargent, T. J. 1997. Two computations to fundzh_TW
dc.relation.reference (參考文獻) social security, Macroeconomic Dynamics,1(1), 7-44.zh_TW
dc.relation.reference (參考文獻) [28] Imrohoroglu, A., Imrohoroglu, S., Joines, D. 1995. A life cycle analysis ofzh_TW
dc.relation.reference (參考文獻) social security, Economic Theory, 6, 83-114.zh_TW
dc.relation.reference (參考文獻) [29] Imrohoroglu, A., Imrohoroglu, S., Joines, D. 1999a. A dynamic stochasticzh_TW
dc.relation.reference (參考文獻) general equilibrium analysis of social security, in Kehoe, T., Prescott, E.,zh_TW
dc.relation.reference (參考文獻) eds., The Discipline of Applied General Equilibrium, Springer-Verlag.zh_TW
dc.relation.reference (參考文獻) 2zh_TW
dc.relation.reference (參考文獻) [30] Josa-Fombellida, R., Rinc-Zapatero, J. P., 2001. Minimization of risks inzh_TW
dc.relation.reference (參考文獻) pension funding by means of contributions and portfolio selection, Insur-zh_TW
dc.relation.reference (參考文獻) ance: Mathematics and Economics, 29, 35-45.zh_TW
dc.relation.reference (參考文獻) [31] Karatzas, I., Lehoczky, J. P., Sethi, S. P., Shreve, S. E., 1986. Explicitzh_TW
dc.relation.reference (參考文獻) solutions of a 30 general consumption investment problem, Mathematics ofzh_TW
dc.relation.reference (參考文獻) Operations Research, 11, 261-294.zh_TW
dc.relation.reference (參考文獻) [32] Koo, H. K. 1998. Consumption and portfolio selection with labor income:zh_TW
dc.relation.reference (參考文獻) a continuous time approach, Mathematical Finance, 8, 49-65.zh_TW
dc.relation.reference (參考文獻) [33] Karatzas, I., Shreve, S. 1991. Brownian Motion and Stochastic Calculus.zh_TW
dc.relation.reference (參考文獻) Springer, New York.zh_TW
dc.relation.reference (參考文獻) [34] Kim, T., Omberg, E., 1996. Dynamic nonmyopic portfolio behavior, Reviewzh_TW
dc.relation.reference (參考文獻) of Financial Studies 9, 141-161.zh_TW
dc.relation.reference (參考文獻) [35] Lioui, A., Poncet, P., 2001. On optimal portfolio choice under stochasticzh_TW
dc.relation.reference (參考文獻) interest rates. Journal of Economic Dynamic and Control 25, 1841-1865.zh_TW
dc.relation.reference (參考文獻) [36] Madsen, J. B. 2002. The share market boom and the recent disin‡ationzh_TW
dc.relation.reference (參考文獻) in the OECD countries: the tax-e¤ects, the in‡ation-illusion, and the risk-zh_TW
dc.relation.reference (參考文獻) aversion hypotheses reconsidered. Quarterly Review of Economics and Fi-zh_TW
dc.relation.reference (參考文獻) nance, 42, 115-141.zh_TW
dc.relation.reference (參考文獻) [37] Markowitz, H. M., 1952. Portfolio selection. Journal of Finance 7(1), 77-91.zh_TW
dc.relation.reference (參考文獻) [38] Markus, R., William, T., Z., 2004. Intertemporal surplus management.zh_TW
dc.relation.reference (參考文獻) Journal of Economic Dynamics and Control 28, 975-990.zh_TW
dc.relation.reference (參考文獻) [39] Menoncin, F., 2002. Optimal portfolio and background risk: an exact andzh_TW
dc.relation.reference (參考文獻) an approximated solution, Insurance: Mathematics and Economics, 31,zh_TW
dc.relation.reference (參考文獻) 249-265.zh_TW
dc.relation.reference (參考文獻) [40] Merton, R. C. 1969. Lifetime portfolio selection under uncertainty: Thezh_TW
dc.relation.reference (參考文獻) continuous time case. Review of Economics and Statistics 51, 247-257.zh_TW
dc.relation.reference (參考文獻) [41] Merton, R. C. 1971. Optimum consumption and portfolio rules in a con-zh_TW
dc.relation.reference (參考文獻) tinuous time model. Journal of Economic Theory 3, 373-413.zh_TW
dc.relation.reference (參考文獻) [42] Merton, R. C. 1990. Continuous-time Finance. Blackwell, Cambridge, MA.zh_TW
dc.relation.reference (參考文獻) [43] Modigliani, F., John, R. A. 1979. In‡ation, rational valuation and the mar-zh_TW
dc.relation.reference (參考文獻) ket. Financial Analysts Journal, 24-44.zh_TW
dc.relation.reference (參考文獻) [44] O’Brien, T., 1986. A stochastic-dynamic approach to pension funding, In-zh_TW
dc.relation.reference (參考文獻) surance: Mathematics and Economics, 5, 141-146.zh_TW
dc.relation.reference (參考文獻) [45] O’Brien, T., 1987. A two-parameter family of pension contribution func-zh_TW
dc.relation.reference (參考文獻) tions and stochastic optimization, Insurance: Mathematics and Economics,zh_TW
dc.relation.reference (參考文獻) 6, 129-134.zh_TW
dc.relation.reference (參考文獻) 3zh_TW
dc.relation.reference (參考文獻) [46] Ritter, J. R., Warr, R. S. 2002. The decline of in‡ation and the bull marketzh_TW
dc.relation.reference (參考文獻) of 1982 to 1999. Journal of Financial and Quantitative Economics, 37, 29-zh_TW
dc.relation.reference (參考文獻) 61.zh_TW
dc.relation.reference (參考文獻) [47] Runggaldier, W. J., 1998. Concept and methods for discrete and continuouszh_TW
dc.relation.reference (參考文獻) time control under uncertainty, Insurance: Mathematics and Economics,zh_TW
dc.relation.reference (參考文獻) 22, 25-39.zh_TW
dc.relation.reference (參考文獻) [48] Rutkowski. M., 1999. Self-…nancing trading strategies for sliding, rolling-zh_TW
dc.relation.reference (參考文獻) horizon, and consol bonds. Mathematical Finance 9, no. 4, 361-365.zh_TW
dc.relation.reference (參考文獻) [49] Samuelson, P., 1969. Lifetime portfolio selection by dynamic stochasticzh_TW
dc.relation.reference (參考文獻) programming, Review of Economics and Statistics, 51, 239-246.zh_TW
dc.relation.reference (參考文獻) [50] Schäl, M., 1998. On piecewise deterministic Markov control processes: con-zh_TW
dc.relation.reference (參考文獻) trol of jumps and of risk processes in insurance, Insurance: Mathematicszh_TW
dc.relation.reference (參考文獻) and Economics, 22, 75-91.zh_TW
dc.relation.reference (參考文獻) [51] Sharpe, W. F., 1991. Capital asset prices with and without negative hold-zh_TW
dc.relation.reference (參考文獻) ings, Journal of Finance, 64, 489-509.zh_TW
dc.relation.reference (參考文獻) [52] Sorensen, C., 1999. Dynamic asset allocation and …xed income manage-zh_TW
dc.relation.reference (參考文獻) ment, Journal of Financial and Quantitative Analysis, 34, 513-531.zh_TW
dc.relation.reference (參考文獻) [53] Vasicek, O. E. 1997. An equilibrium characterization of the term structure.zh_TW
dc.relation.reference (參考文獻) Journal of Financial Economics 5, 177-188.zh_TW
dc.relation.reference (參考文獻) [54] Viceira L. M., 2001. Optimal portfolio choice for long-horizon investorszh_TW
dc.relation.reference (參考文獻) with non-tradable labor income, Journal of Finance, 56, 433-470.zh_TW
dc.relation.reference (參考文獻) [55] Wachter, J. A., 2002. Portfolio and consumption decisions under mean-zh_TW
dc.relation.reference (參考文獻) reverting returns: an exact solution for complete markets, Journal of Fi-zh_TW
dc.relation.reference (參考文獻) nancial and Quantitative Analysis, 37, 63-91.zh_TW
dc.relation.reference (參考文獻) 4zh_TW