scholarly journals Fast and accurate Monte Carlo sampling of first-passage times from Wiener diffusion models

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Jan Drugowitsch
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Sampling ◽  
Diffusion Models ◽  
First Passage Times ◽  
First Passage ◽  
Passage Times

scholarly journals A martingale analysis of first passage times of time-dependent Wiener diffusion models

2017 ◽  
Vol 77 ◽  
pp. 94-110 ◽  
Author(s):  
Vaibhav Srivastava ◽  
Samuel F. Feng ◽  
Jonathan D. Cohen ◽  
Naomi Ehrich Leonard ◽  
Amitai Shenhav
Keyword(s):  
Diffusion Models ◽  
First Passage Times ◽  
Time Dependent ◽  
First Passage ◽  
Passage Times

scholarly journals Fast and accurate calculations for first-passage times in Wiener diffusion models

2019 ◽  
Author(s):  
Danielle Navarro ◽  
Ian Fuss
Keyword(s):  
Probability Density ◽  
Large Time ◽  
Small Time ◽  
Diffusion Models ◽  
First Passage Times ◽  
Response Time Models ◽  
Psychonomic Bulletin ◽  
First Passage ◽  
Perceptual Matching ◽  
Passage Times

We propose a new method for quickly calculating the probability density function for first-passage times in simple Wiener diffusion models, extending an earlier method used by [Van Zandt, T., Colonius, H., & Proctor, R. W. (2000). A comparison of two response-time models applied to perceptual matching. Psychonomic Bulletin & Review, 7, 208–256]. The method relies on the observation that there are two distinct infinite series expansions of this probability density, one of which converges quickly for small time values, while the other converges quickly at large time values. By deriving error bounds associated with finite truncation of either expansion, we are able to determine analytically which of the two versions should be applied in any particular context. The bounds indicate that, even for extremely stringent error tolerances, no more than 8 terms are required to calculate the probability density. By making the calculation of this distribution tractable, the goal is to allow more complex extensions of Wiener diffusion models to be developed.

scholarly journals Applying the Wiener-Hopf Monte Carlo Simulation Technique for Lévy Processes to Path Functionals

2015 ◽  
Vol 52 (1) ◽  
pp. 129-148 ◽  
Author(s):  
Albert Ferreiro-Castilla ◽  
Kees van Schaik
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Lévy Processes ◽  
Levy Processes ◽  
Simulation Technique ◽  
Levy Process ◽  
First Passage Times ◽  
First Passage ◽  
Monte Carlo Simulation Technique ◽  
Passage Times

In this paper we apply the recently established Wiener-Hopf Monte Carlo simulation technique for Lévy processes from Kuznetsov et al. (2011) to path functionals; in particular, first passage times, overshoots, undershoots, and the last maximum before the passage time. Such functionals have many applications, for instance, in finance (the pricing of exotic options in a Lévy model) and insurance (ruin time, debt at ruin, and related quantities for a Lévy insurance risk process). The technique works for any Lévy process whose running infimum and supremum evaluated at an independent exponential time can be sampled from. This includes classic examples such as stable processes, subclasses of spectrally one-sided Lévy processes, and large new families such as meromorphic Lévy processes. Finally, we present some examples. A particular aspect that is illustrated is that the Wiener-Hopf Monte Carlo simulation technique (provided that it applies) performs much better at approximating first passage times than a ‘plain’ Monte Carlo simulation technique based on sampling increments of the Lévy process.

Applying the Wiener-Hopf Monte Carlo Simulation Technique for Lévy Processes to Path Functionals

2015 ◽  
Vol 52 (01) ◽  
pp. 129-148 ◽  
Author(s):  
Albert Ferreiro-Castilla ◽  
Kees van Schaik
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Lévy Processes ◽  
Levy Processes ◽  
Simulation Technique ◽  
Levy Process ◽  
First Passage Times ◽  
First Passage ◽  
Monte Carlo Simulation Technique ◽  
Passage Times

In this paper we apply the recently established Wiener-Hopf Monte Carlo simulation technique for Lévy processes from Kuznetsov et al. (2011) to path functionals; in particular, first passage times, overshoots, undershoots, and the last maximum before the passage time. Such functionals have many applications, for instance, in finance (the pricing of exotic options in a Lévy model) and insurance (ruin time, debt at ruin, and related quantities for a Lévy insurance risk process). The technique works for any Lévy process whose running infimum and supremum evaluated at an independent exponential time can be sampled from. This includes classic examples such as stable processes, subclasses of spectrally one-sided Lévy processes, and large new families such as meromorphic Lévy processes. Finally, we present some examples. A particular aspect that is illustrated is that the Wiener-Hopf Monte Carlo simulation technique (provided that it applies) performs much better at approximating first passage times than a ‘plain’ Monte Carlo simulation technique based on sampling increments of the Lévy process.

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