Name: Prof. C. K. Raju - AlBukhary International University
Title: Non-Normal, Non-Markovian Methods for Predictive Analytics and Risk Measurement
Abstract:
Successful predictive analytics, and the efficient management of risk, both, pre- suppose a good underlying statistical and computational model. However, existing techniques and software for this purpose typically assume stationarity in the time series data they use. Furthermore, they typically estimate the volatility using the sample variance. But these techniques fail if, as happens in practice, the sample comes from a stable distribution, with index of stability α < 2, which lacks a finite second moment. A paradigm shift is required to handle this situation. One can split hairs and try to preserve the conclusion of the central limit theorem by using, say, a truncated Levy distribution; but this is of no practical significance because of the “ultra-slow” convergence to the normal, especially for high-frequency data in the absence of stationarity. I will illustrate some of the possibilities using my software for the numerical solution of stochastic differential equations driven by Levy motion.
Similarly, the customary Markovian assumption, thought to correspond to market efficiency, is open to question; for, even if the market is efficient, it does not operate instantaneously. On the other hand, as the classical theory of functional differential equations (FDEs) informs us, it is dangerous to neglect a delay on account of its smallness. In fact, the novel qualitative features of FDE's point to the need for another paradigm shift, as I have argued in my earlier book Time: Towards a Consistent Theory (Kluwer, 1994), and subsequent publications. I will illustrate some of the novel possibilities, using numerical solutions of retarded FDEs.
Finally, if one does drop various simplifying assumptions, one finds that the computational goals have gone very far ahead of the available “rigorous” mathematics. Under these circumstances, how much reliance should be placed on the results of numerical simulation? In the absence of formal mathematical proof, what is the appropriate way to develop robust and reliable techniques of computation? I will recall some key features of my new philosophy of mathematics called zeroism (as elaborated in my book Cultural Foundations of Mathematics, Pearson, 2007), and how it scores over formalism especially in applications to probabilities. This entails yet another paradigm shift in understanding and interpreting the results of computer simulation. Finally, I will discuss the possibility of exploiting parallelism for faster computation needed for real-time business decisions.
Biography : C. K. Raju holds a PhD from the renowned Indian Statistical Institute, Kolkata. He played a lead role in building India's first parallel supercomputer Param, and has single-handedly built and maintained industrial and pedagogical software packages. His publications have been critically acclaimed at the highest level, and he has authored several path-breaking books. He received the TGA gold medal, in Hungary in 2010, for his work pointing out a mathematical error in Einstein's understanding of relativity.
His structured-time interpretation of quantum mechanics points to a unique way to tackle the decoherence problem of quantum computing. This is linked to his theory of a “tilt in the arrow of time”, and to modification of both Maxwell's equations, and Newtonian gravity using functional differential equations. His new mathematical philosophy of zeroism suits computational mathematics much better than formalism.
A popular teacher, he has lectured live on TV, and has headed the largest university department of computer science in India. He has recently developed an alternative, “decolonised” pedagogy in several areas including mathematics, statistics, physics, and the history and philosophy of science.
He was a Fellow of the Indian Institute of Advanced Study and various other institutions, has helped edit various academic journals, and is currently Vice President of the Indian Social Science Academy. He has lectured in five continents. He has been based in Malaysia for the last few years, first as a Visiting Professor at the Universiti Sains Malaysia, and currently as Professor at the AlBukhary International University.