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Andrei Khrennikov on Negative Probabilities

Over the last few years it has occurred to me that negative probabilities are not necessarily nonsense, and can possibly even be of use in finance. Negative probabilities go back at least to the Nobel prize winner Paul Dirac's introduction of the idea in a paper in 1942. One of today's true probability masters is Andrei Khrennikov, whose first (student) papers on negative and complex probabilities were published in Dokl. Acad. Sc by the recommendation of A. N. Kolmogorov – the founder of modern probability theory. However, Khrennikov did not simply accept the axiomatics of modern probability theory. By looking into the very foundation of probability Khrennikov could no longer exclude negative probabilities. While Nobel prize winners like Dirac and Feynman had considered negative probabilities only as formal quantities useful in certain calculations, Khrennikov found the deep roots of negative probabilities. Based on this he has been one of the most important figures behind the development of a profound mathematical theory of probability, where negative probabilities are just as natural as positive ones.

Andrei Khrennikov is currently a Professor of Applied Mathematics, and the Director of International Center in Mathematical Modeling in Physics and Cognitive Sciences, University of Växjö, Sweden. He has written more than two hundred papers on probability theory, applied mathematics and quantum physics. Many of his ideas in probability ...