Early warning on stock market bubbles via ellipsoidal clustering and inverse problems

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2014

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Kürüm, Efsun

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When a financial bubble bursts, not only a large number of people suffer directly in society, but it also affects the entire economy. Therefore, it is important to develop an early warning using mathematics-supported tools that aims at a detection of bubbles. We introduce a new method which approaches the bubble concept geometrically by determining and evaluating ellipsoids. In fact, we generate a volume-based index via minimum-volume covering ellipsoid clustering method, and in order to visualize these ellipsoids, we utilize Radon transform from the theory of the inverse problems, in the form of figures. Analyses were conducted for US, Japan and China stock markets. In our study, we have observed that when the time approaches bubble-burst time, the volumes of the ellipsoids gradually decrease and, correspondingly, the figures obtained by Radon transform are becoming more “brilliant”, i.e., more strongly warning. The thesis ends with a conclusion and an outlook to future investigations.

Subject Keywords

Stock exchanges., Stock Market Bubble, 1995-2000., Assets (Accounting)., Ellipsoidal calculus., Inverse problems (Differential equations).

URI

http://etd.lib.metu.edu.tr/upload/12617059/index.pdf
https://hdl.handle.net/11511/23476

Collections

Graduate School of Applied Mathematics, Thesis

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Citation Formats

E. Kürüm, “Early warning on stock market bubbles via ellipsoidal clustering and inverse problems,” Ph.D. - Doctoral Program, Middle East Technical University, 2014.