Carr–Nadtochiy’s weak reflection principle for Markov chains on $$\mathbf {Z}^d$$
| Autor: | Yuri Imamura |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Carr Markov chain Applied Mathematics Mathematical finance General Engineering Hitting time 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics Joint probability distribution Lattice (order) 0101 mathematics Algebraic number Brownian motion Mathematics |
| Zdroj: | Japan Journal of Industrial and Applied Mathematics. 38:257-267 |
| ISSN: | 1868-937X 0916-7005 |
| DOI: | 10.1007/s13160-020-00436-w |
| Popis: | 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 $$\mathbf {Z}^d$$ . 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. |
| Databáze: | OpenAIRE |
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