与鞅相关的广义Ornstein-Uhlenbeck过程及其在金融中的应用

doi:10.16088/j.issn.1001-6600.2016.01.013

摘要/Abstract

摘要： 本文研究一个由谱负广义Ornstein-Uhlenbeck过程的恒定水平首达时的二维联合分布及其在这个首达时的原始停止。基于有关Levy过程和GOU过程的一些结果,通过使用鞅和马尔可夫链方法,给出了依据新特殊函数分布的拉普拉斯变换的显式表达式。详细研究了稳定情况下的广义Ornstein-Uhlenbeck过程,给出了计算广义Vasicek 模型中的欧式最大值看涨期权价格的拉普拉斯变换公式,推广了已有结果。

关键词: 鞅, 广义Ornstein-Uhlenbeck过程, Laplace变换, 首达时, 期限结构, 路径依赖期权

Abstract: The two-dimensional joint distribution of the first passage times of spectrally negative generalized Ornstein-Uhlenbeck processes at a constant level and their original stop atthe first passage time, are studied in this paper. Based on some results about Levy and GOU processes, an explicit expression of the Laplace transform of the distribution in terms of new special functions is given by using martingale and Markov chain method. This paper detailedly studies the generalized Ornstein-Uhlenbeck process in the steady state, and provides the Laplasce transformation formula of the European call option price in the generalized Vasicek model, which generalizes the existing results.

Key words: martingales, generalized Ornstein-Uhlenbeck process, Laplace transform, first passage time, term structure, path dependent options

中图分类号:

O211.6

胡华. 与鞅相关的广义Ornstein-Uhlenbeck过程及其在金融中的应用[J]. 广西师范大学学报（自然科学版）, 2016, 34(1): 84-92.

HU Hua. Generalized Ornstein-Uhlenbeck Processes Associatedwith Martingale and Its Application in Finance[J]. Journal of Guangxi Normal University(Natural Science Edition), 2016, 34(1): 84-92.

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