First Passage and Excursion Time Models for Valuing Defaultable Bonds

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

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Credit Gap Risk in a First Passage Time Model with Jumps

SSRN Electronic Journal ◽

10.2139/ssrn.1509491 ◽

2009 ◽

Cited By ~ 1

Author(s):

Natalie Packham ◽

Lutz Schloegl ◽

Wolfgang M. Schmidt

Keyword(s):

First Passage Time ◽

Passage Time ◽

First Passage ◽

Time Model ◽

Gap Risk ◽

Credit Gap

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On the Markov Transition Kernels for First Passage Percolation on the Ladder

Journal of Applied Probability ◽

10.1017/s0021900200007932 ◽

2011 ◽

Vol 48 (02) ◽

pp. 366-388 ◽

Cited By ~ 1

Author(s):

Eckhard Schlemm

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Asymptotic Variance ◽

Almost Sure Convergence ◽

First Passage Percolation ◽

First Passage ◽

Percolation Problem ◽

Vertex Set ◽

Step Transition

We consider the first passage percolation problem on the random graph with vertex set N x {0, 1}, edges joining vertices at a Euclidean distance equal to unity, and independent exponential edge weights. We provide a central limit theorem for the first passage times l n between the vertices (0, 0) and (n, 0), thus extending earlier results about the almost-sure convergence of l n / n as n → ∞. We use generating function techniques to compute the n-step transition kernels of a closely related Markov chain which can be used to explicitly calculate the asymptotic variance in the central limit theorem.

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