An approximation for the inverse first passage time problem

Abstract

We propose an approximation for the inverse first passage time problem. It is similar in spirit and method to the tangent approximation for the original first passage time problem. We provide evidence that the technique is quite accurate in many cases. We also identify some cases where the approximation performs poorly.

The inverse first-passage time problem as hydrodynamic limit of a particle system

“…The author of [18] transfers the latter method to the case of reflected Brownian motion. The authors of [19] propose a modified VIE method by estimating the integral equation by using the empirical distribution of g. A further approach can be found in [4], which is related to the tangent-method for the first-passage time problem. Bounds for the discretization error of the methods of [3] were given therein, but a rigorous study and comparison of the existing methods for the solutions of the inverse first-passage time problem has yet to be provided.…”

“…A first application was proposed by [1] and [2] in the context of credit risk, in order The inverse first-passage time problem and particle system to use the solutions to model the default time of a company as first-passage time, when data about the distribution of the default time is given. Since then, several methods have been found in order to simulate the unknown solutions of the inverse first-passage time problem [3], [4]. Regarding this, another computational objective is often to sample from the conditional distribution…”

Explicit solution of an inverse first-passage time problem for Lévy processes and counterparty credit risk

“…Chen et al [11] prove existence and uniqueness of the IFPT of an arbitrary continuous CDF on R + for a diffusion with smooth bounded coefficients and strictly positive volatility function. In [3,17,18,35,36], a number of methods have been developed to compute this boundary, which is in general nonlinear. Zucca and Sacerdote [36] analyse a Monte Carlo approximation method and a method based on the discretization of the Volterra integral equation satisfied by the boundary, which was derived in Peskir [33], while related integral equations are studied in Jaimungal et al [20].…”