Carr-Nadtochiy’s weak reflection principle for Markov chains on Z^d
Carr-Nadtochiy’s weak reflection principle for Markov chains on Z^d
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Z^d 上马尔可夫链的 Carr-Nadtochiy 弱反射原理
DOI：
10.1007/s13160-020-00436-w
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发表时间：
2020
影响因子：
0.9
通讯作者：
Yuri Imamura
中科院分区：
文献类型：
--
作者：
Gaina Daniel;Nakamura Masaki;Ogata Kazuhiro;Futatsugi Kokichi;Yuri Imamura
布朗运动的反射原理给出了一种计算击中时间和一维边际的联合分布的方法。卡尔-纳托奇变换是在这方面推广反射原理的公式。这种转换起源于金融数学文献中的一种对冲所谓障碍期权的方法。仅对一维扩散过程证明了变换的存在性。本文证明了一类相当一般的多维格上马氏链的存在性。困难在于反射边界不是一个单点集，与一维情况相反。本文用代数方法解决了这一问题。
The reflection principle for Brownian motion gives a way to calculate the joint distribution of a hitting time and a one dimensional marginal. The Carr–Nadtochiy transform is a formulation that generalizes the reflection principle in this respect. The transform originated from a way to hedge so-called barrier options in the literature of financial mathematics. The existence of the transform has been established only for one dimensional diffusion processes. In the present paper, the existence is proved for a fairly general class of Markov chains in the multi dimensional lattice. The difficulty is that the reflection boundary is not a one-point set, contrasting the one dimensional cases. It is solved in this paper by looking at the problem in an algebraic way.