Dan Pirjol

Dan Pirjol is a researcher whose work spans theoretical particle physics and mathematical finance. Stevens Institute of Technology's profile describes research in derivatives pricing, hedging and risk management using asymptotic analysis and applied probability. Its linked publication record directly associates him with the2001 physics paper by Christian W. Bauer, Sean Fleming, Pirjol and Iain W. Stewart.^[ref]

That paper develops an effective field theory for energetic quarks and soft/collinear gluons and uses scale-separated calculations of heavy-to-light processes. It forms part of the development of soft-collinear effective theory.^[ref] The institutional link is important here: the physics author and the financial-mathematics researcher are not being identified by name similarity alone.

An original payoff calculation illustrates one mathematical feature of the option models named in his research profile. An arithmetic-average Asian option with observation values $S_1,\dots ,S_n$ and strike $K$ can have payoffFor stipulated observations90,90,90and130 with $K=100$, the arithmetic mean is100 and this payoff is zero. A European option using only the terminal value130 instead has call payoff30. Four observations130,130,130and130 instead give Asian payoff30 with the same terminal price. Thus identical terminal prices need not determine an average-dependent payoff. This is an explanatory calculation, not a pricing result attributed to Pirjol or a recommendation about a financial product.

His profile's focus on asymptotic analysis concerns mathematical approximations to such stochastic-model quantities, while the earlier physics work organizes approximations through scale hierarchies. The applications differ, but both require an explicit model and a justified regime for the approximation.