Title: Applying Dynamic Non-Classical Arithmetic (DNA) to Probability and Finance

Abstract: Non-classical arithmetics replace ordinary addition and/or multiplication in standard arithmetic with other binary operations called pseudo-addition and multiplication. Dynamic non-classical arithmetic (DNA) allows a different non-classical arithmetic to be used at each time. We apply DNA to enhance our understanding of the logistic distribution and entropy in probability theory. We also apply DNA to develop a novel arbitrage-free option pricing model in finance. Under our approach, European option valuation reduces to pseudo-addition of spot and strike, while Bermudan option valuation reduces to repeated pseudo-addition. Simple and realistic closed-form formulas are easily generated in both cases.

Bio: Dr. Peter Carr is the Chair of the Finance and Risk Engineering Department at NYU Tandon School of Engineering. He has headed various quant groups in the financial industry for the last twenty years. He also presently serves as a trustee for the National Museum of Mathematics and WorldQuant University. Prior to joining the financial industry, Dr. Carr was a finance professor for 8 years at Cornell University, after obtaining his Ph.D. from UCLA in 1989. He has over 85 publications in academic and industry-oriented journals and serves as an associate editor for 8 journals related to mathematical finance. He was selected as Quant of the Year by Risk Magazine in 2003 and Financial Engineer of the Year by IAQF/Sungard in 2010. From 2011 to 2014, Dr. Carr was included in Institutional Investor's Tech 50, an annual listing of the 50 most influential people in financial technology.

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