Abstract
Stochastic differential equations (SDEs) rapidly become one of the most well-known formats in which to express such diverse mathematical models under uncertainty such as financial models, neural systems, behavioral and neural responses, human reactions and behaviors. They belong to the main methods to describe randomness of a dynamical model today. In a financial system, different kinds of SDEs have been elaborated to model various financial assets. On the other hand, economists have conducted research on several empirical phenomena regarding the behaviour of individual investors, such as how their emotions and opinions influence their decisions. All those emotions and opinions are described by the word Sentiment. In finance, stochastic changes might occur according to investors’ sentiment levels. In our study, we aim to represent the mutual effects between some financial process and investors’ sentiment with constructing a coupled system of non-autonomous SDEs, evolving in time. These equations are hard to assess and solve. Therefore, we express them in a simplified manner by discretization and Multivariate Adaptive Regression Splines (MARS) model. MARS is a strong method for flexible regression and classification with interactive variables. Hereby, we treat time as another spatial variable. Eventually, we present a modern application with real-world data. This study finishes with a conclusion and an outlook towards future studies.
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References
Ardalan, K. (2018). Neurofinance versus the efficient markets hypothesis. Neurofinance Versus the Efficient Markets Hypothesis, 35, 170–176.
Baker, M., & Wurgler, J. (2017). Investor sentiment and the cross-section of stock returns. Internet: http://pages.stern.nyu.edu/jwurgler/data/. Accessed January 20, 2017.
Baker, M., & Wurgler, J. (2006). Investor sentiment and the cross-section of stock returns. The Journal of Finance, Wiley Online Library, 61(4), 1645–1680.
Baker, M., & Wurgler, J. (2007). Investor sentiment in the stock market. The Journal of Economic Perspectives, American Economic Association, 21(2), 129–151.
Bloomberg. Internet: https://www.bloomberg.com/quote/CPURNSA:IND. Accessed March 13, 2017.
Bormann, S. K. (2013). Sentiment indices on financial markets: What do they measure?. Economics Discussion Papers, University of Tartu, Estonia.
Çevik, A., Weber, G. W., Eyüpoğlu, B. M., & Oğuz, K. K. (2017). Voxel-MARS: A method for early detection of Alzheimer’s disease by classification of structural brain MRI. Annals of Operations Research, 258(1), 31–57.
Cobb, L. (1981). Stochastic differential equations for the social sciences (pp. 37–68)., Mathematical frontiers of the social and policy sciences Boulder, CO: Westview Press and American Association for the Advancement of Science.
Colander, D. (2000). The complexity vision and the teaching of economics. Cheltenham: Edward Elgar Publishing.
Friedman, J., Hastie, T., & Tibshirani, R. (2001). The elements of statistical learning., Springer series in statistics, 1 New York: Springer.
Frydman, C. D. (2012). Essays in neurofinance. Ph.D. thesis, California Institute of Technology, Pasadena, USA.
Frydman, C., & Camerer, C. F. (2016). The psychology and neuroscience of financial decision making. Trends in Cognitive Sciences Elsevier, 20(9), 661–675.
Hubbard, T. P., & Saglam, Y. (2006). Stochastic processes, ito calculus, and applications in economics., Lecture notes Iowa: Department of Mathematics, University of Iowa.
Jeanblanc, M., Yor, M., & Chesney, M. (2009). Mathematical methods for financial markets. Berlin: Springer.
Kalaycı, B. (2017). Identification of coupled systems of stochastic differential equations in finance including investor sentiment by multivariate adaptive regression splines. M.Sc. thesis, Institute of Applied Mathematics, METU, Ankara, Turkey, July.
Khalilpourazari, S., Soltanzadeh, S., Weber, G. W., & Roy, S. K. (2019). Designing an efficient blood supply chain network in crisis: Neural learning, optimization and case study. Annals of Operations Research, 289, 1–30.
Korn, R., & Korn, E. (2001). Option pricing and portfolio optimization: Modern methods of financial mathematics, 31. Providence: American Mathematical Soc.
Kropat, E., Tikidji-Hamburyan, R. A., & Weber, G. W. (2017). Special issue “Operations research in neuroscience”. Annals OR, 258(1), 1–4.
Kuhnen, C. M., & Knutson, B. (2005). The neural basis of financial risk taking. Neuron, 47(5), 763–770.
Lamberton, D., & Lapeyre, B. (2007). Introduction to stochastic calculus applied to finance. Boca Raton: CRC Press.
MARS from Salford Systems. Internet: http://www.salfordsystems/products/mars/. Accessed July 23, 2017.
Muhammad, N., Maheran, N., et al. (2009). Behavioural finance vs traditional finance. Advanced Management, 2(6), 1–10.
Øksendal, B. (2003). Stochastic differential equations (pp. 65–84). Berlin: Springer.
Özmen, A. (2010). Robust conic quadratic programming in applied to quality improvement—a robustification of CMARS. M.Sc. thesis, Institute of Applied Mathematics, METU, Ankara, Turkey.
Özmen, A. (2016). Robust optimization of spline models and complex regulatory networks. Berlin: Springer.
Rilling, J. K., & Sanfey, G. A. (2011). The neuroscience of social decision-making. Annual Review of Psychology, 62, 23–48.
Ritter, J. R. (2003). Behavioral finance. Pacific-Basin Finance Journal, 11(4), 429–437.
Sadeghnia, M., Hooshmand, A. B., & Habib, N. (2013). Behavioral finance and neurofinance and research conducted in this area. Interdisciplinary Journal of Contemporary Research in Business, 4, 793.
Sauer, T. (2012). Numerical solution of stochastic differential equations in finance. In Handbook of computational finance (pp. 529–550). Berlin: Springer.
Shariff, M. Z., Al-Khasawneh, J., & Al-Mutawa, M. (2012). Risk and reward: A neurofinance perspective. International Review of Business Research Papers, 8(6), 126–133.
Taylan, P., Özkurt, F. Y., & Weber, G. W. (2010). A new approach to multivariate adaptive regression splines by using Tikhonov regularization and continuous optimization. TOP, 18(2), 377–395.
Taylan, P., & Weber, G. W. (2008). Organization in finance prepared by stochastic differential equations with additive and nonlinear models and continuous optimization. Organizacija, 41(5), 185–193.
Taylan, P., & Weber, G. W. (2008). Organization in finance prepared by stochastic differential equations with additive and nonlinear models and continuous optimization. Organizacija, Versita, 41(5), 185–193.
Thaler, R. H. (2010). The end of behavioral finance. Financial Analysts Journal, CFA Institute (pp. 13–23).
Tseng, K. C. (2006). Behavioral finance, bounded rationality, neuro-finance, and traditional finance. Investment Management and Financial Innovations, 3(4), 7–18.
Vasile, D., & Sebastian, T. C. (2007). Neurofinance—Getting an Insight into the Trader’s Mind. Neuroscience, 27(31), 8159–8160.
Wang, X. (2015). Online nonparametric estimation of stochastic differential equations. Electronic Thesis and Dissertation Repository, The University of Western Ontario.
Weber, G. W., Taylan, P., Görgülü, Z. K., Rahman, H. Abd., & Bahar, A. (2011). Parameter estimation in stochastic differential equations, corresponds to chapter 51 of the book. In Dynamics, games and science II (in Honor of Maurício Peixoto and David Rand), Springer-Verlag 2011, Springer proceeding in mathematics (pp. 703–733), ISBN: 978-3-342-14787-6; M. Peixoto, D. Rand and A. Pinto.
Weber, G. W., Taylan, P., Yılıdrak, K., & Görgülü, Z. K. (2010). Financial regression and organization. Special Issue on Optimization in Finance, DCDIS-B, 17(16), 149–174.
Zhang, C. (2008). Defining, modeling, and measuring investor sentiment. Berkeley: Department of Economics, University of California.
Zouaoui, M., Nouyrigat, G., & Beer, F. (2011). How does investor sentiment affect stock market crises? Financial Review, Wiley Online Library, 46(4), 723–747.
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Kalaycı, B., Özmen, A. & Weber, GW. Mutual relevance of investor sentiment and finance by modeling coupled stochastic systems with MARS. Ann Oper Res 295, 183–206 (2020). https://doi.org/10.1007/s10479-020-03757-8
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DOI: https://doi.org/10.1007/s10479-020-03757-8