Efficient Estimation of One-Dimensional Diffusion First Passage Time Densities via Monte Carlo Simulation

Ichiba, Tomoyuki; Kardaras, Constantinos

doi:10.1017/s0021900200008251

Cited by 7 publications

(13 citation statements)

References 16 publications

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“…As an alternative, we provide the perturbed FPTD in the next proposition. Note that, in the case I = (a, +∞), the drift function in (25) and its derivative are bounded on I. According to Proposition 2.1, the perturbation series converges.…”

Section: Ornstein-uhlenbeck Processmentioning

confidence: 92%

Explicit asymptotics on first passage times of diffusion processes

Dassios

2020

Adv. Appl. Probab.

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We introduce a unified framework for solving first passage times of time-homogeneous diffusion processes. Using potential theory and perturbation theory, we are able to deduce closed-form truncated probability densities, as asymptotics or approximations to the original first passage time densities, for single-side level crossing problems. The framework is applicable to diffusion processes with continuous drift functions; in particular, for bounded drift functions, we show that the perturbation series converges. In the present paper, we demonstrate examples of applying our framework to the Ornstein–Uhlenbeck, Bessel, exponential-Shiryaev, and hypergeometric diffusion processes (the latter two being previously studied by Dassios and Li (2018) and Borodin (2009), respectively). The purpose of this paper is to provide a fast and accurate approach to estimating first passage time densities of various diffusion processes.

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Section: Ornstein-uhlenbeck Processmentioning

confidence: 92%

Explicit asymptotics on first passage times of diffusion processes

Dassios

2020

Adv. Appl. Probab.

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“…Grisanov's transformation permits to link the diffusion process X solution of (1.2) to the Brownian motion (a slight modification of Proposition 2.1 in [22]).…”

Section: Girsanov's Transformationmentioning

confidence: 99%

“…Step 1. Let us first present a quite different expression for η(t) defined by (1.5) (these arguments were already developed in [22]). Let us define…”

Section: Algorithm (A1)mentioning

confidence: 99%

“…• Ichiba & Kardaras [22] proposed an efficient estimation of the first-passage density using on one hand Girsanov's transformation and on the second hand a Monte Carlo procedure in order to estimate the Radon-Nikodym derivative which involves a Bessel bridge of dimension δ = 3. This interesting approach permits to deal with a large family of diffusion processes but introduces a Monte-Carlo approximation error.…”

Section: Introductionmentioning

confidence: 99%

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Exact Simulation of the First-Passage Time of Diffusions

Herrmann

Zucca

2019

J Sci Comput

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Since diffusion processes arise in so many different fields, efficient technics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations of the first-passage times as a by-product. For efficiency reasons, it is particularly challenging to simulate directly this hitting time by avoiding to construct the whole paths. In the Brownian case, the distribution of the first-passage time is explicitly known and can be easily used for simulation purposes. The authors introduce a new rejection sampling algorithm which permits to perform an exact simulation of the first-passage time for general one-dimensional diffusion processes. The efficiency of the method, which is essentially based on Girsanov's transformation, is described through theoretical results and numerical examples.

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“…Some works have already been done in the context of smooth drift and diffusion coefficient by Gobet and Menozzi [6,7]. A recent paper by Ichiba and Kardaras [9] also uses the representation of the passage density as the mean of a three dimensional Brownian motion.…”

Section: Introductionmentioning

confidence: 99%

Simulation of hitting times for Bessel processes with non-integer dimension

Deaconu¹,

Herrmann²

2017

Bernoulli

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In this paper we pursue and complete the study of the simulation of the hitting time of some given boundaries for Bessel processes. These problems are of great interest in many application fields as finance and neurosciences. In a previous work [3], the authors introduced a new method for the simulation of hitting times for Bessel processes with integer dimension. The method was based mainly on the explicit formula for the distribution of the hitting time and on the connexion between the Bessel process and the Euclidean norm of the Brownian motion. This method does not apply anymore for a non integer dimension. In this paper we consider the simulation of the hitting time of Bessel processes with non integer dimension and provide a new algorithm by using the additivity property of the laws of squared Bessel processes. We split each simulation step in two parts: one is using the integer dimension case and the other one considers hitting time of a Bessel process starting from zero.

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Efficient Estimation of One-Dimensional Diffusion First Passage Time Densities via Monte Carlo Simulation

Cited by 7 publications

References 16 publications

Explicit asymptotics on first passage times of diffusion processes

Explicit asymptotics on first passage times of diffusion processes

Exact Simulation of the First-Passage Time of Diffusions

Simulation of hitting times for Bessel processes with non-integer dimension

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