Journal of Applied Probability

On the monitoring error of the supremum of a normal jump diffusion process

Ao Chen, Liming Feng, and Renming Song

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Abstract

We derive an expansion for the (expected) difference between the continuously monitored supremum and evenly monitored discrete maximum over a finite time horizon of a jump diffusion process with independent and identically distributed normal jump sizes. The monitoring error is of the form a0 / N1/2 + a1 / N3/2 + · · · + b1 / N + b2 / N2 + b4 / N4 + · · ·, where N is the number of monitoring intervals. We obtain explicit expressions for the coefficients {a0, a1, . . . , b1, b2, . . .}. In particular, a0 is proportional to the value of the Riemann zeta function at ½, a well-known fact that has been observed for Brownian motion in applied probability and mathematical finance.

Article information

Source
J. Appl. Probab., Volume 48, Number 4 (2011), 1021-1034.

Dates
First available in Project Euclid: 16 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1324046016

Digital Object Identifier
doi:10.1239/jap/1324046016

Mathematical Reviews number (MathSciNet)
MR2896665

Zentralblatt MATH identifier
1250.60036

Subjects
Primary: 60G51: Processes with independent increments; Lévy processes 60J75: Jump processes 91G60: Numerical methods (including Monte Carlo methods)
Secondary: 65C20: Models, numerical methods [See also 68U20]

Keywords
Normal jump diffusion process supremum discrete monitoring Spitzer's identity Euler-Maclaurin formula Riemann zeta function Lerch transcendent

Citation

Chen, Ao; Feng, Liming; Song, Renming. On the monitoring error of the supremum of a normal jump diffusion process. J. Appl. Probab. 48 (2011), no. 4, 1021--1034. doi:10.1239/jap/1324046016. https://projecteuclid.org/euclid.jap/1324046016


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