A general lower bound of parameter estimation for reflected Ornstein–Uhlenbeck processes

2016 ◽  
Vol 53 (1) ◽  
pp. 22-32 ◽  
Author(s):  
Qing-Pei Zang ◽  
Li-Xin Zhang
Keyword(s):  
Parameter Estimation ◽  
Lower Bound ◽  
Unknown Parameter ◽  
Extended Model ◽  
Rate Model ◽  
Short Term ◽  
Uhlenbeck Process ◽  
Mild Conditions ◽  
Ornstein Uhlenbeck Process ◽  
Interest Rate Model

AbstractA reflected Ornstein–Uhlenbeck process is a process that returns continuously and immediately to the interior of the state space when it attains a certain boundary. It is an extended model of the traditional Ornstein–Uhlenbeck process being extensively used in finance as a one-factor short-term interest rate model. Under some mild conditions, this paper is devoted to the study of the analogue of the Cramer–Rao lower bound of a general class of parameter estimation of the unknown parameter in reflected Ornstein–Uhlenbeck processes.

scholarly journals Lévy Interest Rate Models with a Long Memory

Risks ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 2
Author(s):  
Donatien Hainaut
Keyword(s):  
Interest Rate ◽  
Long Memory ◽  
Sample Path ◽  
Rate Model ◽  
Short Term ◽  
Uhlenbeck Process ◽  
Interest Rate Models ◽  
Infinite Dimensional ◽  
Bond Options ◽  
Interest Rate Model

This article proposes an interest rate model ruled by mean reverting Lévy processes with a sub-exponential memory of their sample path. This feature is achieved by considering an Ornstein–Uhlenbeck process in which the exponential decaying kernel is replaced by a Mittag–Leffler function. Based on a representation in term of an infinite dimensional Markov processes, we present the main characteristics of bonds and short-term rates in this setting. Their dynamics under risk neutral and forward measures are studied. Finally, bond options are valued with a discretization scheme and a discrete Fourier’s transform.

scholarly journals A Lower Bound for the First Passage Time Density of the Suprathreshold Ornstein-Uhlenbeck Process

2011 ◽  
Vol 48 (02) ◽  
pp. 420-434 ◽  
Author(s):  
Peter J. Thomas
Keyword(s):  
Lower Bound ◽  
First Passage Time ◽  
Passage Time ◽  
Initial Condition ◽  
First Passage ◽  
Uhlenbeck Process ◽  
Fire Model ◽  
Integrate And Fire ◽  
Ornstein Uhlenbeck Process ◽  
Time Density

We prove that the first passage time density ρ(t) for an Ornstein-Uhlenbeck processX(t) obeying dX= -βXdt+ σdWto reach a fixed threshold θ from a suprathreshold initial conditionx0> θ > 0 has a lower bound of the form ρ(t) >kexp[-pe6βt] for positive constantskandpfor timestexceeding some positive valueu. We obtain explicit expressions fork,p, anduin terms of β, σ,x0, and θ, and discuss the application of the results to the synchronization of periodically forced stochastic leaky integrate-and-fire model neurons.

scholarly journals Berry–Esséen bound for the parameter estimation of fractional Ornstein–Uhlenbeck processes

2019 ◽  
Vol 20 (04) ◽  
pp. 2050023 ◽  
Author(s):  
Yong Chen ◽  
Nenghui Kuang ◽  
Ying Li
Keyword(s):  
Parameter Estimation ◽  
Brownian Motion ◽  
Continuous Time ◽  
Index Formula ◽  
Hurst Index ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Time Observation ◽  
Statistical Estimations ◽  
Drift Parameter

For an Ornstein–Uhlenbeck process driven by fractional Brownian motion with Hurst index [Formula: see text], we show the Berry–Esséen bound of the least squares estimator of the drift parameter based on the continuous-time observation. We use an approach based on Malliavin calculus given by Kim and Park [Optimal Berry–Esséen bound for statistical estimations and its application to SPDE, J. Multivariate Anal. 155 (2017) 284–304].

Quantile sensitivity estimation for dependent sequences

2016 ◽  
Vol 53 (3) ◽  
pp. 715-732
Author(s):  
Guangxin Jiang ◽  
Michael C. Fu
Keyword(s):  
Limit Theorem ◽  
Weak Consistency ◽  
Infinitesimal Perturbation Analysis ◽  
Regenerative Processes ◽  
Uhlenbeck Process ◽  
Numerical Examples ◽  
Mild Conditions ◽  
Sensitivity Estimation ◽  
Ornstein Uhlenbeck Process ◽  
Infinitesimal Perturbation

AbstractIn this paper we estimate quantile sensitivities for dependent sequences via infinitesimal perturbation analysis, and prove asymptotic unbiasedness, weak consistency, and a central limit theorem for the estimators under some mild conditions. Two common cases, the regenerative setting and ϕ-mixing, are analyzed further, and a new batched estimator is constructed based on regenerative cycles for regenerative processes. Two numerical examples, the G/G/1 queue and the Ornstein–Uhlenbeck process, are given to show the effectiveness of the estimator.

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