本文探討投資人面對景氣循環下如何進行股票投資決策，藉由隨機動態規劃法建構代表性投資人的決策問題，並推導出資產配置決策的最適解。當經濟成長率愈高、勞動投入與資本投入成長率愈低時，投資人持有愈多股票。我們支持投資人仍會基於生產性質的差異而有不同最適資產配置，風險趨避程度高的投資人配置較少的股票比重。

This study analyzes optimal decisions of asset allocation for stock investors under the consideration of the business cycle. By a stochastic dynamic programming approach to establish a problem model for investors, we derive the optimal solutions for asset allocations. As the economic growth rate is higher, as the labor’s and the capital’s growth rate are lower, investors tend to hold more weight on stock. We find that the optimal asset allocation varies with the characteristics of production inputs. An investor who has a higher degree of risk-aversion put less weight on wealth on the risky assets.

第一章 緒論 1
第一節 研究背景 1
第二節 研究目的 3
第三節 研究貢獻 3
第四節 研究架構 4
第二章 文獻探討 5
第一節 景氣循環 5
第二節 投資組合 6
第三節 動態規劃以及隨機最適控制 6
第三章 研究方法 9
第一節 模型設定 9
第二節 景氣循環之隨機過程 9
第三節 資產配置 13
第四節 效用函數 18
第四章 數值分析 21
第一節 經濟成長率對於景氣影響係數之分析 21
第二節 實體生產投入成長率對於景氣影響係數之分析 22
第三節 景氣成份風險對於避險係數之分析 23
第四節 風險性資產對於避險係數之分析 24
第五節 景氣的循環作用之分析 24
第五章 結論 27
參考文獻 29
附錄1. 景氣循環隨機過程 32
附錄2. 最適控制條件的推導 36
附錄3. 最適控制決策的推導 39
附錄圖表 42
圖一：景氣影響係數與經濟成長率對最適投資比率 42
圖二：景氣影響係數以及實體資本成長率對最適投資比率 43
圖三：景氣影響係數以及勞動成長率對最適投資比率 44
圖四：風險趨避係數與經濟風險對最適投資比率 45
圖五：風險趨避係數與資本風險對最適投資比率 46
圖六：風險趨避係數與勞動風險對最適投資比率 47
圖七：景氣影響係數與風險趨避係數對最適投資比率 48
圖八：證券風險與風險趨避係數對最適投資比率 49
表一：景氣繁榮以及景氣衰退間對最適投資比率 50

Bellman, E. B. (1957). Dynamic programming. Princeton University Press, 339 pages.
Bertsimas, D., & Lo, A. W. (1998). Optimal control of execution costs, Journal of Finance Markets 1, 1-50.
Black, F., Scholes, M., & Jensen, M. (1972). The Capital-Asset Pricing Model: Some empirical tests, Studies in the Theory of Capital Markets, 79-121.
Chalmers, J., Kaul, A., & Phillips, B. (2013). The wisdom of crowds: Mutual fund investors’ aggregate asset allocation decisions, Journal of Banking & Finance, 37(9), 3318-3333.
Chiu, M. C., & Wong, H. Y. (2014). Mean-variance portfolio selection with correlation risk, Journal of Computational and Applied Mathematics, 263, 432-444.
Chilarescu, C., & Vaneecloo, N., (2007). A Stochastic Approach to the Cobb-Douglas Production Function, Economics Bulletin, 3(9), 1-8.
Drazen, A. (1981). Inflation and capital accumulation under a finite horizon, Journal of Monetary Economics, 8(2), 247-260.
Fischer, S. (1975). The Demand for Index Bonds, Journal of Political Economy, 83(3). 509-534.
Fama, E. F. & French, K. R. (2004). The Capital Asset Pricing Model: Theory and Evidence, Journal of Economic Perspectives, 18(3), 25-46.
French, K. R., William Schwert, G., & Stambaugh, R. F. (1987). Expected stock returns and volatility, Journal of Financial Economics, 19(1), 3-29.
Goetzman, W. N., & Ibbotson, R. G. (1994). Do winners repeat? Pattern in mutual fund performance, The Journal of Portfolio Management 20(2), 9-18.
Ippolito, R. A., (1992). Consumer reaction to measure of poor quality: Evidence from the mutual fund industry, The Journal of Law and Economics, 35(1), 45-70.
John,. C. C., & Huang, C. (1989). Optimal consumption and portfolio policies when asset prices follow a diffusion process, Journal of Economic Theory, 49(1), 33–83.
Jun, X., Li, M., & Shi, J. (2014). Volatile market condition and investor clientele effects on mutual fund flow performance relationship, Pacific-Basin Finance Journal, 29, 310-334.
Keynes, J. M. (1936). The General Theory of Employment, Interest and Money. England: Palgrave Macmillan.
Kwak, M., & Lim, B. H. (2014). Optimal portfolio selection with life insurance under inflation risk, Journal of Banking & Finance, 46, 59-71.
Lioui, A. (2013). Time consistent vs. time inconsistent dynamic asset allocation: Some utility cost calculations for mean variance preferences, Journal of Economic Dynamics & Control, 37(5), 1066-1096.
Lynch, A. W., & Tan, S. (2011). Labor income dynamics at business-cycle frequencies: Implications for portfolio choice, Journal of Financial Economics, 101(2), 333–359.
Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets, The Review of Economics and Statistics, 47(1), 13-37.
Lucas, J &. Robert E. (1988). On the mechanics of economic development Journal of Monetary Economics, 22(1), 3-42.
Liu, J., Longstaff, F. A., & Pan, J. (2003). Dynamic asset allocation with event risk, The Journal of Finance, 58, 231-259.
Liu, J. (2007). Portfolio selection in stochastic environments, Review of Financial Studies, 20(1), 1–39.
Lu, J., & Li, X. (2021). Identifying the fair value of Sharpe ratio by an option valuation approach, The Quarterly Review of Economics and Finance, 82, 63–70.
Li, S., Liu, S., Zhou, Y., Wu, Y., & Ge, X. (2020). Optimal portfolio selection of mean-variance utility with stochastic interest rate, Journal of Function Spaces, 1-10. DOI : 10.1155/2020/3153297
Liu, H., Loewenstein, M. (2013). Market Crashes, correlated illiquidity, and portfolio choice, Management Science, 59(3), 715-732.
Liang, Y., (2010). An application of Merton’s portfolio selection problem to the case with a zero recovery bond, International Journal of Innovative
Computing, Information and Control, 7(1), 141-149.
Markowitz, H. M. (1952). Portfolio Selection, Journal of Finance, 7(1), 77-91.
Mossin, J. (1966). Equilibrium in a Capital Asset Market, Econometrica, 34, 768-783.
Merton, R.C. (1973). An intertemporal capital asset pricing model, Econometrica, 41(5), 867-887.
Perold, A. F. (2004). The Capital Asset Pricing Model, The Journal of Economic Perspectives 18(3), 3-24.
Pliska, S. R. (1986). A stochastic calculus model of continuous trading: Optimal portfolios, Mathematic Operation Research, 11(2), 371-382.
Poterba, J. M., and Summers, L. H. (1986). The persistence of volatility and stock market fluctuations, American Economic Review, 76(5), 1142-1151. DOI :10.3386/w1462
Sharpe, W. F. (1964). Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk, Journal of Finance, 19(3), 425-442.
Solow R. M. (1956). A Contribution to the Theory of Economic Growth. The Quarterly Journal of Economics, 70(1), 65-94.
Swan, T. W. (1956). Economic Growth and Capital Accumulation, The Economic Record, 32(2), 334-361.
Treynor, J.L. (1965). How to Rate Management of Investment Funds. Harvard Business Review,43, 63-75.