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On the two-boundary first-crossing-time problem for diffusion processes

Published online by Cambridge University Press:  14 July 2016

A. Buonocore,
V. Giorno,
A. G. Nobile and
L. M. Ricciardi
A. Buonocore*
Affiliation:
University of Naples
V. Giorno*
Affiliation:
University of Salerno
A. G. Nobile*
Affiliation:
University of Salerno
L. M. Ricciardi*
Affiliation:
University of Naples
*
∗ Postal address: Dipartimento di Matematica e Applicazioni, University of Naples, Via Mezzocannone 8, 80134 Naples, Italy.
∗∗ Postal address: Dipartimento di Informatica e Applicazioni, University of Salerno, 84100 Salerno, Italy.
∗∗ Postal address: Dipartimento di Informatica e Applicazioni, University of Salerno, 84100 Salerno, Italy.
∗ Postal address: Dipartimento di Matematica e Applicazioni, University of Naples, Via Mezzocannone 8, 80134 Naples, Italy.
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Abstract

The first-crossing-time problem through two time-dependent boundaries for one-dimensional diffusion processes is considered. The first-crossing p.d.f.'s from below and from above are proved to satisfy a new system of Volterra integral equations of the second kind involving two arbitrary continuous functions. By a suitable choice of such functions a system of continuous-kernel integral equations is obtained and an efficient algorithm for its solution is provided. Finally, conditions on the drift and infinitesimal variance of the diffusion process are given such that the system of integral equations reduces to a non-singular single integral equation for the first-crossing-time p.d.f.

Keywords

VARYING BOUNDARIESVOLTERRA INTEGRAL EQUATIONS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 1 , March 1990, pp. 102 - 114
Copyright
Copyright © Applied Probability Trust 1990 

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References

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