Identification of coupled systems of stochastic differential equations in finance including investor sentiment by multivariate adaptive regression splines

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2017
Kalaycı, Betül
Stochastic Differential Equations (SDEs) rapidly become the most well-known format in which to express such diverse mathematical models under uncertainty such as financial models, neural systems, micro-economic systems, and human behaviour. They are one of 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. Emotions can affect the way of thinking. A negative state leads to be risk-averse, while a positive state leads to be ambitious, and to act in a risky way even. 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 of an approximation by discretization and Multivariate Adaptive Regression Splines (MARS) model. MARS is a strong method for flexible regression and classification with interactive variables, based on high-dimensional and big data. Hereby, we treat time as another spatial variable. Afterwards, we will present a modern application with real-world data. The thesis finishes with a conclusion and an outlook towards future studies.

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Citation Formats
B. Kalaycı, “Identification of coupled systems of stochastic differential equations in finance including investor sentiment by multivariate adaptive regression splines,” M.S. - Master of Science, Middle East Technical University, 2017.