KILLED BROWNIAN MOTION WITH A PRESCRIBED LIFETIME DISTRIBUTION AND MODELS OF DEFAULT
成果类型：
Article
署名作者：
Ettinger, Boris; Evans, Steven N.; Hening, Alexandru
署名单位：
Princeton University; University of California System; University of California Berkeley; University of Oxford
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/12-AAP902
发表日期：
2014
页码：
1-33
关键词：
摘要：
The inverse first passage time problem asks whether, for a Brownian motion B and a nonnegative random variable zeta, there exists a time-varying barrier b such that P{B-s > b(s), O <= s <= t} > P{zeta < t}. We study a smoothed version of this problem and ask whether there is a barrier b such that E[exp(-lambda integral(t)(O) psi (B-s - b(s)) ds)] = P{zeta > t}, where lambda is a killing rate parameter, and psi : R -> [0, 1] is a nonincreasing function. We prove that if psi is suitably smooth, the function t bar right arrow P{zeta > t} is twice continuously differentiable, and the condition 0 < - dlog P{zeta>t}/dt < lambda holds for the hazard rate of zeta then there exists a unique continuously differentiable function b solving the smoothed problem. We show how this result leads to flexible models of default for which it is possible to compute expected values of contingent claims.