A Note on First Passage Times in Birth and Death and Nonnegative Diffusion Processes.

1979 ◽  
Author(s):  
Cyrus Derman ◽  
Sheldon M. Ross ◽  
Zvi Schechner
Keyword(s):  
Diffusion Processes ◽  
First Passage Times ◽  
First Passage ◽  
Passage Times

A note on first passage times in birth and death and nonnegative diffusion processes

1983 ◽  
Vol 30 (2) ◽  
pp. 283-285 ◽  
Author(s):  
Cyrus Derman ◽  
Sheldon M. Ross ◽  
Zvi Schechner
Keyword(s):  
Diffusion Processes ◽  
First Passage Times ◽  
First Passage ◽  
Passage Times

An improved technique for the simulation of first passage times for diffusion processes

1999 ◽  
Vol 28 (4) ◽  
pp. 1135-1163 ◽  
Author(s):  
Maria Teresa Giraudo ◽  
Laura Sacerdote
Keyword(s):  
Diffusion Processes ◽  
First Passage Times ◽  
First Passage ◽  
Improved Technique ◽  
Passage Times

More general problems on first-passage times for diffusion processes: A new version of the fptdApprox R package

2014 ◽  
Vol 244 ◽  
pp. 432-446 ◽  
Author(s):  
P. Román-Román ◽  
J.J. Serrano-Pérez ◽  
F. Torres-Ruiz
Keyword(s):  
Diffusion Processes ◽  
R Package ◽  
First Passage Times ◽  
First Passage ◽  
Passage Times

First passage times of a jump diffusion process

2003 ◽  
Vol 35 (2) ◽  
pp. 504-531 ◽  
Author(s):  
S. G. Kou ◽  
Hui Wang
Keyword(s):  
Diffusion Process ◽  
Diffusion Processes ◽  
Jump Diffusion ◽  
First Passage Times ◽  
First Passage ◽  
Jump Diffusion Processes ◽  
Lookback Options ◽  
Double Exponential ◽  
Jump Diffusion Process ◽  
Passage Times

This paper studies the first passage times to flat boundaries for a double exponential jump diffusion process, which consists of a continuous part driven by a Brownian motion and a jump part with jump sizes having a double exponential distribution. Explicit solutions of the Laplace transforms, of both the distribution of the first passage times and the joint distribution of the process and its running maxima, are obtained. Because of the overshoot problems associated with general jump diffusion processes, the double exponential jump diffusion process offers a rare case in which analytical solutions for the first passage times are feasible. In addition, it leads to several interesting probabilistic results. Numerical examples are also given. The finance applications include pricing barrier and lookback options.

Solutions for some diffusion processes with two barriers

1970 ◽  
Vol 7 (2) ◽  
pp. 423-431 ◽  
Author(s):  
A. L. Sweet ◽  
J. C. Hardin
Keyword(s):  
Diffusion Processes ◽  
Separation Of Variables ◽  
Probability Density Functions ◽  
First Passage Times ◽  
Mathematical Methods ◽  
First Passage ◽  
Forward Equation ◽  
Forward Equations ◽  
Two Barriers ◽  
Passage Times

Use is often made of the Wiener and Ornstein-Uhlenbeck (O.U.) processes in various applications of stochastic processes to problems of engineering interest. These applications frequently involve the presence of barriers. Although mathematical methods for solving Kolmogorov's forward equation for the above processes have previously been discussed ([1], [2]), many solutions for problems with two barriers do not seem to be available in the literature. Instead, one finds solutions for unrestricted processes or simulation used in place of analytical solutions in various applications ([3], [4], [5]). In this paper, solutions of Kolmogorov's forward equations in the presence of constant absorbing and/or reflecting barriers are obtained by means of separation of variables. This enables one to obtain expressions for the probability density functions for first passage times when absorbing barriers are present. The solution for the O.U. process is used to obtain a result of Breiman's [6] concerning first passage times.

Order statistics for first passage times in one-dimensional diffusion processes

1996 ◽  
Vol 85 (3-4) ◽  
pp. 501-512 ◽  
Author(s):  
S. Bravo Yuste ◽  
Katja Lindenberg
Keyword(s):  
Order Statistics ◽  
Diffusion Processes ◽  
First Passage Times ◽  
First Passage ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Passage Times

Solutions for some diffusion processes with two barriers

1970 ◽  
Vol 7 (02) ◽  
pp. 423-431 ◽  
Author(s):  
A. L. Sweet ◽  
J. C. Hardin
Keyword(s):  
Diffusion Processes ◽  
Separation Of Variables ◽  
Probability Density Functions ◽  
First Passage Times ◽  
Mathematical Methods ◽  
First Passage ◽  
Forward Equation ◽  
Forward Equations ◽  
Two Barriers ◽  
Passage Times

Use is often made of the Wiener and Ornstein-Uhlenbeck (O.U.) processes in various applications of stochastic processes to problems of engineering interest. These applications frequently involve the presence of barriers. Although mathematical methods for solving Kolmogorov's forward equation for the above processes have previously been discussed ([1], [2]), many solutions for problems with two barriers do not seem to be available in the literature. Instead, one finds solutions for unrestricted processes or simulation used in place of analytical solutions in various applications ([3], [4], [5]). In this paper, solutions of Kolmogorov's forward equations in the presence of constant absorbing and/or reflecting barriers are obtained by means of separation of variables. This enables one to obtain expressions for the probability density functions for first passage times when absorbing barriers are present. The solution for the O.U. process is used to obtain a result of Breiman's [6] concerning first passage times.

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