= Dan Pirjol
{c}
\b[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>.<Dan Pirjol profile at Stevens Institute of Technology>[Research and identity-linked institutional bibliography]{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>.<An effective field theory for collinear and soft gluons: heavy to light decays by Christian W. Bauer and others>[byline and Abstract]{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 $S_1,\ldots,S_n$ and strike $K$ can have payoff
$$
\max\left(\frac1n\sum_{j=1}^{n}S_j-K,0\right).
$$
For 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.
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