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Ordered by a blend of empirical rigor (60%) and math complexity (40%).

On the Weak Error for Local Stochastic Volatility Models

Local stochastic volatility refers to a popular model class in applied mathematical finance that allows for “calibration-on-the-fly”, typically via a particle method, derived from a formal McKean-Vlasov equation. Well-posedness of this limit is a well-known problem in the field; the general case is

Lab Rats Math 9 Rigor 4 ·  June 12, 2025

Non-decreasing martingale couplings

For many examples of couples $(μ,ν)$ of probability measures on the real line in the convex order, we observe numerically that the Hobson and Neuberger martingale coupling, which maximizes for $ρ=1$ the integral of $|y-x|^ρ$ with respect to any martingale coupling between $μ$ and $ν$, is still a max

Lab Rats Math 8.5 Rigor 2.5 ·  April 30, 2023

An extension of martingale transport and stability in robust finance

While many questions in robust finance can be posed in the martingale optimal transport framework or its weak extension, others like the subreplication price of VIX futures, the robust pricing of American options or the construction of shadow couplings necessitate additional information to be incorp

Lab Rats Math 9.2 Rigor 1.5 ·  April 19, 2023

Maximal Martingale Wasserstein Inequality

In this note, we complete the analysis of the Martingale Wasserstein Inequality started in arXiv:2011.11599 by checking that this inequality fails in dimension $d\ge 2$ when the integrability parameter $ρ$ belongs to $[1,2)$ while a stronger Maximal Martingale Wasserstein Inequality holds whatever t

Lab Rats Math 8.5 Rigor 1 ·  October 12, 2023

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