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

Markovian projections for Itô semimartingales with jumps

Given a general Itô semimartingale, its Markovian projection is an Itô process, with Markovian differential characteristics, that matches the one-dimensional marginal laws of the original process. We construct Markovian projections for Itô semimartingales with jumps, whose flows of one-dimensional m

Lab Rats Math 8.5 Rigor 2.5 ·  March 24, 2024

Inverting the Markovian projection for pure jump processes

Markovian projections arise in problems where we aim to mimic the one-dimensional marginal laws of an Itô semimartingale by using another Itô process with Markovian dynamics. In applications, Markovian projections are useful in calibrating jump-diffusion models with both local and stochastic feature

Lab Rats Math 8.5 Rigor 1.5 ·  December 5, 2024

Markovian projections for functionals of Itô semimartingales with jumps

Given an Itô semimartingale $X$, its Markovian projection is an Itô semimartingale $\widehat{X}$, with Markovian differential characteristics, that matches the one-dimensional marginal laws of $X$. One may even require certain functionals of the two processes to have the same fixed-time marginals, a

Lab Rats Math 9 Rigor 1 ·  June 1, 2025

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