有跳跃的伊托半马勒的马尔可夫投影

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-03-24 DOI:arxiv-2403.15980

Martin Larsson, Shukun Long

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引用次数: 0

摘要

给定一个一般的It\^o semimartingale，其马尔可夫投影是一个具有马尔可夫微分特征的It\^oprocess，它与原始过程的一维边际规律相匹配。我们为有跳跃的 It\o semimartingales 构建了马尔可夫投影，它的一维边际律流是非局部福克--普朗克--科尔莫哥罗夫方程（FPKEs）的解。作为应用，我们展示了马尔可夫投影如何出现在建立具有局部和随机特征的校准扩散/跳跃模型中。

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Markovian projections for Itô semimartingales with jumps

Given a general It\^o semimartingale, its Markovian projection is an It\^o process, with Markovian differential characteristics, that matches the one-dimensional marginal laws of the original process. We construct Markovian projections for It\^o semimartingales with jumps, whose flows of one-dimensional marginal laws are solutions to non-local Fokker--Planck--Kolmogorov equations (FPKEs). As an application, we show how Markovian projections appear in building calibrated diffusion/jump models with both local and stochastic features.

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arXiv - QuantFin - Mathematical Finance

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