A singular perturbation approach to first passage times for Markov jump processes

1986 ◽  
Vol 42 (1-2) ◽  
pp. 169-184 ◽  
Author(s):  
C. Knessl ◽  
B. J. Matkowsky ◽  
Z. Schuss ◽  
C. Tier
Keyword(s):  
Singular Perturbation ◽  
First Passage Times ◽  
Jump Processes ◽  
Perturbation Approach ◽  
Markov Jump ◽  
First Passage ◽  
Markov Jump Processes ◽  
Passage Times

Asymptotic solution of the Kramers-Moyal equation and first-passage times for Markov jump processes

1984 ◽  
Vol 29 (6) ◽  
pp. 3359-3369 ◽  
Author(s):  
B. J. Matkowsky ◽  
Z. Schuss ◽  
C. Knessl ◽  
C. Tier ◽  
M. Mangel
Keyword(s):  
Asymptotic Solution ◽  
First Passage Times ◽  
Jump Processes ◽  
Markov Jump ◽  
First Passage ◽  
Markov Jump Processes ◽  
Passage Times

On the first-passage times of pure jump processes

1988 ◽  
Vol 25 (3) ◽  
pp. 501-509 ◽  
Author(s):  
Moshe Shaked ◽  
J. George Shanthikumar
Keyword(s):  
Failure Rate ◽  
Sufficient Conditions ◽  
Jump Process ◽  
First Passage Times ◽  
Jump Processes ◽  
First Passage ◽  
Increasing Failure Rate ◽  
Passage Times

Let Tx be the time it takes for a pure jump process, which starts at 0, to cross a threshold x > 0. Sufficient conditions on the parameters of this process under which Tx has increasing failure rate average (IFRA), increasing failure rate (IFR) or logconcave density (PF2) are identified. The conditions for IFRA are weaker than those of Drosen (1986). Sufficient conditions on the parameter of a pure jump process for Tx to the IFR or PF2 are not available in the literature.

On the first-passage times of pure jump processes

1988 ◽  
Vol 25 (03) ◽  
pp. 501-509 ◽  
Author(s):  
Moshe Shared ◽  
J. George Shanthikumar
Keyword(s):  
Failure Rate ◽  
Sufficient Conditions ◽  
Jump Process ◽  
First Passage Times ◽  
Jump Processes ◽  
First Passage ◽  
Increasing Failure Rate ◽  
Passage Times

Let Tx be the time it takes for a pure jump process, which starts at 0, to cross a threshold x > 0. Sufficient conditions on the parameters of this process under which Tx has increasing failure rate average (IFRA), increasing failure rate (IFR) or logconcave density (PF2) are identified. The conditions for IFRA are weaker than those of Drosen (1986). Sufficient conditions on the parameter of a pure jump process for Tx to the IFR or PF2 are not available in the literature.

scholarly journals The First Passage Time Problem for Mixed-Exponential Jump Processes with Applications in Insurance and Finance

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Chuancun Yin ◽  
Yuzhen Wen ◽  
Zhaojun Zong ◽  
Ying Shen
Keyword(s):  
Risk Model ◽  
Diffusion Processes ◽  
First Passage Time ◽  
Laplace Transforms ◽  
First Passage Times ◽  
Jump Processes ◽  
Closed Form Expression ◽  
First Passage ◽  
Time Problem ◽  
Passage Times

This paper studies the first passage times to constant boundaries for mixed-exponential jump diffusion processes. Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the first passage times and undershoot (overshoot) are obtained. As applications, we present explicit expression of the Gerber-Shiu functions for surplus processes with two-sided jumps, present the analytical solutions for popular path-dependent options such as lookback and barrier options in terms of Laplace transforms, and give a closed-form expression on the price of the zero-coupon bond under a structural credit risk model with jumps.

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