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

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

2009-05-12

arxiv.org/abs/0905.1975v1

Mathematics

Probability

Scientific paper

In this paper we derive the density $\varphi$ of the first time $T$ that a continuous martingale $M$ with non-random quadratic variation $_\cdot:=\int_0^\cdot h^2(u)du$ hits a moving boundary $f$ which is twice continuously differentiable, and $f'/h\in\mathbb{C}^2[0,\infty)$. 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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