On the first passage time density of a continuous Martingale over a moving boundary

2009/05/12 by Gerardo Hernandez-del-Valle, Hernandez-del-Valle, Gerardo
Mathematics · #45D05 #45G15 (Secondary) #60J60 (Primary) #60J65 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #math.AP #math.PR #msc:45D05 #msc:45G15 #msc:60J60 #msc:60J65

paper · pdf · doi:10.48550/arxiv.0905.1975

arxiv created 2009/05/12 · arxiv updated 2009/12/01

Abstract

In this paper we derive the density φ of the first time T that a continuous martingale M with non-random quadratic variation <M>_⋅:=∫₀^⋅ h²(u)du hits a moving boundary f which is twice continuously differentiable, and f'/h∈ℂ²[0,∞). Thus, this work is an extension to case in which M is in fact a one-dimensional standard Brownian motion B, as studied in Hernandez-del-Valle (2007).

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