A Numeraire-Independent Version of the Fundamental Theorem of Asset Pricing
The Fundamental Theorems of Asset Pricing are aptly-named results that show the relationship between absence of arbitrage and the martingale property. These theorems are fundamental to mathematical finance in that they provide the bridge between the mathematics and the finance: on the one side, the mathematical objects of stochastic processes and martingale measures; on the other the financial ideas of trading strategies and arbitrage. We aim to widen the bridge to cover cleanly the case when there are multiple financial assets, any of which may potentially lose all value relative to the others. To do this we shift away from having a pre-determined numeraire to a more symmetrical point of view where all assets have equal priority.
Joint work with Johannes Ruf and Sergio Pulido.
Biography
Dr. Travis Fisher is an Executive Director at Morgan Stanley, where he leads global modeling efforts for the foreign exchange (FX) options business. He joined Morgan Stanley in 2010. Prior to that he worked at Bloomberg LP, where he focused on FX, equity, and commodity options modeling. Dr. Fisher received his Ph.D. in Mathematics in 2006 from Pennsylvania State University with thesis work on Dynamical Systems. He holds Bachelor’s degrees in Mathematics and Computer Science from the University of Nebraska.
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