 On the Markovian projection in the Brunick–Shreve mimicking resultMartin Forde Statistics & Probability Letters, 2014, vol. 85, issue C, 98-105 Abstract: For a one-dimensional Itô process Xt=∫0tσsdWs and a general FtX-adapted non-decreasing path-dependent functional Yt, we derive a number of forward equations for the characteristic function of (Xt,Yt) for absolutely and non absolutely continuous functionals Yt. The functional Yt can be the maximum, the minimum, the local time, the quadratic variation, the occupation time or a general additive functional of X. Inverting the forward equation, we obtain a new Fourier-based method for computing the Markovian projection E(σt2|Xt,Yt) explicitly from the marginals of (Xt,Yt), which can be viewed as a natural extension of the Dupire formula for local volatility models; E(σt2|Xt,Yt) is a fundamental quantity in the important mimicking theorems in Brunick and Shreve (2013). We also establish mimicking theorems for the case when Y is the local time or the quadratic variation of X (which is not covered by Brunick and Shreve (2013)), and we derive similar results for trivariate Markovian projections. Keywords: Mimicking; Diffusion process; Local volatility models; Markovian projection (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:85:y:2014:i:c:p:98-105 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spl.2013.11.005 Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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