傳統資產定價模型主要考慮風險，而忽略了機率本身的不確定性，即模糊性。本研究採用台灣加權指數作為研究對象，參考了Brenner and Izhakian (2018)提出的實證方法來測量台灣市場中的模糊性程度，並從台灣的市場數據中評估投資者對模糊性的態度。實證結果顯示，模糊性在股票市場中具有價格，且當預期的有利報酬機率較高時，投資者對模糊性表現出厭惡態度。此外，本研究嘗試將模糊性作為一種新指標，並將其引入神經網路與長短期記憶(LSTM)機器學習模型，以觀察其對股票價格預測的影響。結果顯示，加入模糊性後，機器學習模型的預測準確度有提升的趨勢。

Traditional asset pricing models primarily focus on risk, often neglecting the uncertainty inherent in probabilities, known as ambiguity. This research examines the Taiwan Weighted Index, using the empirical method by Brenner and Izhakian (2018) to quantify the level of ambiguity in the Taiwanese market. By analyzing market data from Taiwan, the study evaluates investor attitudes towards ambiguity. The findings indicate that ambiguity is indeed reflected in stock market prices, and investors show aversion to ambiguity when the likelihood of favorable returns is high. Furthermore, this study explores incorporating ambiguity as a new indicator into neural network and long short-term memory (LSTM) machine learning models to assess its impact on stock price predictions. The results indicate an improvement in prediction accuracy for machine learning models with the inclusion of ambiguity.

參考文獻
Augustin, P., & Izhakian, Y. (2020). Ambiguity, volatility, and credit risk. The review of financial studies, 33(4), 1618-1672.
Black, F. (1976). Studies of stock market volatility changes. Proceedings of the American Statistical Association, Business & Economic Statistics Section, 1976.
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 81(3), 637-654.
Brenner, M., & Izhakian, Y. (2012). Asset Pricing and Ambiguity: Empirical Evidence, working paper.
Brenner, M., & Izhakian, Y. (2018). Asset pricing and ambiguity: Empirical evidence. Journal of Financial Economics, 130(3), 503-531.
Campbell, J. Y., & Hentschel, L. (1992). No news is good news: An asymmetric model of changing volatility in stock returns. Journal of Financial Economics, 31(3), 281-318. https://doi.org/https://doi.org/10.1016/0304-405X(92)90037-X
Drechsler, I. (2013). Uncertainty, time‐varying fear, and asset prices. The Journal of Finance, 68(5), 1843-1889.
Epstein, L. G., & Schneider, M. (2003). Recursive multiple-priors. Journal of Economic Theory, 113(1), 1-31.
Epstein, L. G., & Schneider, M. (2008). Ambiguity, Information Quality, and Asset Pricing. The Journal of Finance, 63(1), 197-228. https://doi.org/https://doi.org/10.1111/j.1540-6261.2008.01314.x
Fischer, T., & Krauss, C. (2018). Deep learning with long short-term memory networks for financial market predictions. European journal of operational research, 270(2), 654-669.
French, K. R., Schwert, G. W., & Stambaugh, R. F. (1987). Expected stock returns and volatility. Journal of Financial Economics, 19(1), 3-29. https://doi.org/https://doi.org/10.1016/0304-405X(87)90026-2
Gagliardini, P., Porchia, P., & Trojani, F. (2008). Ambiguity aversion and the term structure of interest rates. The review of financial studies, 22(10), 4157-4188.
Ghysels, E., Santa-Clara, P., & Valkanov, R. (2005). There is a risk-return trade-off after all. Journal of Financial Economics, 76(3), 509-548. https://doi.org/https://doi.org/10.1016/j.jfineco.2004.03.008
Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. The Journal of Finance, 48(5), 1779-1801.
Guo, H., & Whitelaw, R. F. (2006). Uncovering the Risk–Return Relation in the Stock Market. The Journal of Finance, 61(3), 1433-1463. https://doi.org/https://doi.org/10.1111/j.1540-6261.2006.00877.x
Harvey, C. R. (2001). The specification of conditional expectations. Journal of Empirical Finance, 8(5), 573-637.
Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory. Neural computation, 9(8), 1735-1780.
Izhakian, Y. Y. (2012). Ambiguity Measurement. Available at SSRN 1938628.
Jahan-Parvar, M. R., & Liu, H. (2014). Ambiguity aversion and asset prices in production economies. The review of financial studies, 27(10), 3060-3097.
Jeong, D., Kim, H., & Park, J. Y. (2015). Does ambiguity matter? Estimating asset pricing models with a multiple-priors recursive utility. Journal of Financial Economics, 115(2), 361-382.
Ju, N., & Miao, J. (2012). Ambiguity, learning, and asset returns. Econometrica, 80(2), 559-591.
Kahneman, D., & Tversky, A. (2013). Prospect theory: An analysis of decision under risk. In Handbook of the fundamentals of financial decision making: Part I (pp. 99-127). World Scientific.
Klibanoff, P., Marinacci, M., & Mukerji, S. (2005). A smooth model of decision making under ambiguity. Econometrica, 73(6), 1849-1892.
Kumbure, M. M., Lohrmann, C., Luukka, P., & Porras, J. (2022). Machine learning techniques and data for stock market forecasting: A literature review. Expert Systems with Applications, 197, 116659.
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.
Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77-91. https://doi.org/10.2307/2975974
McCulloch, W. S., & Pitts, W. (1943). A logical calculus of the ideas immanent in nervous activity. The bulletin of mathematical biophysics, 5, 115-133.
Merton, R. C. (1980). On estimating the expected return on the market: An exploratory investigation. Journal of Financial Economics, 8(4), 323-361. https://doi.org/https://doi.org/10.1016/0304-405X(80)90007-0
Minsky, M., & Papert, S. (1969). An introduction to computational geometry. Cambridge tiass., HIT, 479(480), 104.
Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica: Journal of the econometric society, 347-370.
Pástor, Ľ., Sinha, M., & Swaminathan, B. (2008). Estimating the Intertemporal Risk–Return Tradeoff Using the Implied Cost of Capital. The Journal of Finance, 63(6), 2859-2897. https://doi.org/https://doi.org/10.1111/j.1540-6261.2008.01415.x
Rosenblatt, F. (1958). The perceptron: a probabilistic model for information storage and organization in the brain. Psychological review, 65(6), 386.
Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning representations by back-propagating errors. Nature, 323(6088), 533-536. https://doi.org/10.1038/323533a0
Scholes, M., & Williams, J. (1977). Estimating betas from nonsynchronous data. Journal of Financial Economics, 5(3), 309-327.
Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of Finance, 19(3), 425-442.
Welch, I., & Goyal, A. (2007). A Comprehensive Look at The Empirical Performance of Equity Premium Prediction. The review of financial studies, 21(4), 1455-1508. https://doi.org/10.1093/rfs/hhm014
Yu, J., & Yuan, Y. (2011). Investor sentiment and the mean–variance relation. Journal of Financial Economics, 100(2), 367-381. https://doi.org/https://doi.org/10.1016/j.jfineco.2010.10.011