## Bernoulli

• Bernoulli
• Volume 22, Number 2 (2016), 794-856.

### On the exact and $\varepsilon$-strong simulation of (jump) diffusions

#### Abstract

This paper introduces a framework for simulating finite dimensional representations of (jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in such a way that the sample path can be restored at any finite collection of time points. Within this framework we extend existing exact algorithms and introduce novel adaptive approaches. We consider an application of the methodology developed within this paper which allows the simulation of upper and lower bounding processes which almost surely constrain (jump) diffusion sample paths to any specified tolerance. We demonstrate the efficacy of our approach by showing that with finite computation it is possible to determine whether or not sample paths cross various irregular barriers, simulate to any specified tolerance the first hitting time of the irregular barrier and simulate killed diffusion sample paths.

#### Article information

Source
Bernoulli, Volume 22, Number 2 (2016), 794-856.

Dates
Revised: April 2014
First available in Project Euclid: 9 November 2015

https://projecteuclid.org/euclid.bj/1447077762

Digital Object Identifier
doi:10.3150/14-BEJ676

Mathematical Reviews number (MathSciNet)
MR3449801

Zentralblatt MATH identifier
1343.60099

#### Citation

Pollock, Murray; Johansen, Adam M.; Roberts, Gareth O. On the exact and $\varepsilon$-strong simulation of (jump) diffusions. Bernoulli 22 (2016), no. 2, 794--856. doi:10.3150/14-BEJ676. https://projecteuclid.org/euclid.bj/1447077762

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