关于平方贝塞尔过程的若干积分泛函

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2012-09-21 DOI:10.1080/17442508.2015.1026344

U. Çetin

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引用次数: 4

摘要

对于一个平方贝塞尔过程，研究了的联合定律的拉普拉斯变换，其中的第一次撞击时间为，并且是相对于X的历史可测的随机变量，直到。然后使用这些结果的一个子集来解决相关的小球问题，并确定迭代对数的Chung定律。也被认为是一个纯粹的不连续递增马尔可夫过程，并找到了它的无穷小发生器。然后，这些发现被用来为一类基于利率的奇特衍生品定价，并确定一些价格略低于实际价值的看跌期权价格的渐近性。

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On certain integral functionals of squared Bessel processes

For a squared Bessel process, , the Laplace transforms of joint laws of are studied where is the first hitting time of by and is a random variable measurable with respect to the history of X until . A subset of these results are then used to solve the associated small ball problems for and to determine a Chung's law of the iterated logarithm. is also considered as a purely discontinuous increasing Markov process and its infinitesimal generator is found. The findings are then used to price a class of exotic derivatives on interest rates and to determine the asymptotics for the prices of some put options that are only slightly in-the-money.

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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.