scholarly journals ON OPTIMAL THRESHOLDS FOR PAIRS TRADING IN A ONE-DIMENSIONAL DIFFUSION MODEL

2021 ◽  
pp. 1-19
Author(s):  
MASAAKI FUKASAWA ◽  
HITOMI MAEDA ◽  
JUN SEKINE
Keyword(s):  
Diffusion Model ◽  
First Passage Time ◽  
Passage Time ◽  
Threshold Strategy ◽  
Pairs Trading ◽  
One Dimensional ◽  
Long Run ◽  
Optimal Thresholds ◽  
Ergodic Diffusion

Abstract We study the static maximization of long-term averaged profit, when optimal preset thresholds are determined to describe a pairs trading strategy in a general one-dimensional ergodic diffusion model of a stochastic spread process. An explicit formula for the expected value of a certain first passage time is given, which is used to derive a simple equation for determining the optimal thresholds. Asymptotic arbitrage in the long run of the threshold strategy is observed.

On optimal thresholds for pairs trading in a one-dimensional diffusion model

2021 ◽  
Vol 63 ◽  
pp. 104-122
Author(s):  
Masaaki Fukasawa ◽  
Hitomi Maeda ◽  
Jun Sekine
Keyword(s):  
Diffusion Model ◽  
First Passage Time ◽  
Passage Time ◽  
Threshold Strategy ◽  
Pairs Trading ◽  
One Dimensional ◽  
Long Run ◽  
Optimal Thresholds ◽  
Ergodic Diffusion

We study the static maximization of long-term averaged profit, when optimal preset thresholds are determined to describe a pairs trading strategy in a general one-dimensional ergodic diffusion model of a stochastic spread process. An explicit formula for the expected value of a certain first passage time is given, which is used to derive a simple equation for determining the optimal thresholds. Asymptotic arbitrage in the long run of the threshold strategy is observed. doi:10.1017/S1446181121000298

scholarly journals Indoor radon concentration and a diffusion model in dwellings situated in a subalkaline granitoid area, Southern Brazil

2021 ◽  
Vol 80 (17) ◽  
Author(s):  
G. Romero-Mujalli ◽  
A. Roisenberg ◽  
A. Cordova-Gonzalez ◽  
P. H. P. Stefano
Keyword(s):  
Diffusion Model ◽  
Indoor Radon ◽  
Southern Brazil ◽  
High Concentration ◽  
Indoor Radon Concentration ◽  
One Dimensional ◽  
Environmental Limits ◽  
Radon Measurements ◽  
Cr 39 Detectors

AbstractRadon (Rn), a radioactive element, has especial interest in medical geology because long-term exposure to high concentration is related to lung cancer. In this study, outdoor and indoor radon measurements were conducted in dwellings of the Piquiri Syenite Massif, located in southern Brazil, given the relative high Rn content in soils of this region. Measurements were done using CR-39 detectors and placing them inside and outside dwellings. Moreover, a one-dimensional diffusion model was performed in order to quantify the natural transport of Rn to the air in confined and aerated environments. Results indicate that the region presents relatively low air Rn concentrations, within the environmental limits; however, the health risk might increase in confined and ill-ventilated environments because of transfer from soil and exhalation from ornamental rock-material often found inside dwellings. The main north facies of the syenite, where most of the rock extractions are located, was found to have the highest air Rn concentration because of the higher soil Rn concentration, compared to other facies of the syenite.

First-passage-time densities for time-non-homogeneous diffusion processes

1997 ◽  
Vol 34 (3) ◽  
pp. 623-631 ◽  
Author(s):  
R. Gutiérrez ◽  
L. M. Ricciardi ◽  
P. Román ◽  
F. Torres
Keyword(s):  
Diffusion Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Continuous Functions ◽  
Probability Density Functions ◽  
Density Functions ◽  
First Passage ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Natural Boundaries

In this paper we study a Volterra integral equation of the second kind, including two arbitrary continuous functions, in order to determine first-passage-time probability density functions through time-dependent boundaries for time-non-homogeneous one-dimensional diffusion processes with natural boundaries. These results generalize those which were obtained for time-homogeneous diffusion processes by Giorno et al. [3], and for some particular classes of time-non-homogeneous diffusion processes by Gutiérrez et al. [4], [5].

scholarly journals The First Passage Time and the Dividend Value Function for One-Dimensional Diffusion Processes between Two Reflecting Barriers

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Chuancun Yin ◽  
Huiqing Wang
Keyword(s):  
Boundary Conditions ◽  
Value Function ◽  
Diffusion Processes ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
One Dimensional ◽  
The Laplace Transform ◽  
The Value Function ◽  
Reflecting Barriers

We consider the general one-dimensional time-homogeneous regular diffusion process between two reflecting barriers. An approach based on the Itô formula with corresponding boundary conditions allows us to derive the differential equations with boundary conditions for the Laplace transform of the first passage time and the value function. As examples, the explicit solutions of them for several popular diffusions are obtained. In addition, some applications to risk theory are considered.

scholarly journals LQG Homing in a Finite Time Interval

2011 ◽  
Vol 2011 ◽  
pp. 1-3 ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Optimal Control ◽  
Diffusion Process ◽  
First Passage Time ◽  
Passage Time ◽  
Time Interval ◽  
Finite Time Interval ◽  
First Passage ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Fixed Constant

LetX(t)be a controlled one-dimensional diffusion process having constant infinitesimal variance. We consider the problem of optimally controllingX(t)until timeT(x)=min{T1(x),t1}, whereT1(x)is the first-passage time of the process to a given boundary andt1is a fixed constant. The optimal control is obtained explicitly in the particular case whenX(t)is a controlled Wiener process.

Moments of the first-passage time of a Wiener process with drift between two elastic barriers

1995 ◽  
Vol 32 (4) ◽  
pp. 1007-1013 ◽  
Author(s):  
Marco Dominé
Keyword(s):  
Wiener Process ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
One Dimensional ◽  
Special Cases ◽  
Backward Equation ◽  
The One ◽  
First Passage Problem ◽  
Reflecting Barriers

The first-passage problem for the one-dimensional Wiener process with drift in the presence of elastic boundaries is considered. We use the Kolmogorov backward equation with corresponding boundary conditions to derive explicit closed-form expressions for the expected value and the variance of the first-passage time. Special cases with pure absorbing and/or reflecting barriers arise for a certain choice of a parameter constellation.

First-Passage Time for Oscillators With Nonlinear Damping

1978 ◽  
Vol 45 (1) ◽  
pp. 175-180 ◽  
Author(s):  
J. B. Roberts
Keyword(s):  
First Passage Time ◽  
Digital Simulation ◽  
Planck Equation ◽  
Passage Time ◽  
Nonlinear Damping ◽  
First Passage ◽  
One Dimensional ◽  
Fokker Planck Equation ◽  
First Passage Failure ◽  
Fokker Planck

A simple numerical scheme is proposed for computing the probability of first passage failure, P(T), in an interval O-T, for oscillators with nonlinear damping. The method depends on the fact that, when the damping is light, the amplitude envelope, A(t), can be accurately approximated as a one-dimensional Markov process. Hence, estimates of P(T) are found, for both single and double-sided barriers, by solving the Fokker-Planck equation for A(t) with an appropriate absorbing barrier. The numerical solution of the Fokker-Planck equation is greatly simplified by using a discrete time random walk analog of A(t), with appropriate statistical properties. Results obtained by this method are compared with corresponding digital simulation estimates, in typical cases.

Sign in / Sign up

Export Citation Format

Share Document