Applied Probability

Fundamental Theorem of Asset Pricing, the Hedging Problem and Maximal Claims in Financial Markets with Short Sales Prohibitions

January, 2014


This paper consists of two parts. In the first part we prove the fundamental theorem of asset pricing under short sales prohibitions in continuous-time financial models where asset prices are driven by nonnegative, locally bounded semimartingales. A key step in this proof is an extension of a well-known result of Ansel and Stricker. In the second part we study the hedging problem in these models and connect it to a properly defined property of "maximality" of contingent claims.

The Probability Conflation: A Reply

January, 2023


We respond to Tetlock et al. (2022) showing 1) how expert judgment fails to reflect tail risk, 2) the lack of compatibility between forecasting tournaments and tail risk assessment methods (such as extreme value theory).More importantly, we communicate a new result showing a greater gap between the properties of tail expectation and those of the corresponding probability.

Foundations of the Theory of Probability - DSA ADS Course 2023

DSA ADS Course 2023

This DSA ADS course is part of a series of courses that demonstrate how to use applied data science with high performance compute and high quality data to optimize decision making in real world scenarios.

Discuss the foundations of probability theory and apply to real world scenarios.

In depth review of classic textbook "Foundations of the Theory of Probability" by Kolmogorov.