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http://hdl.handle.net/2445/193773
Title: | Dyson type formula for pure jump Lévy processes with some applications to finance |
Author: | Jin, Sixian Schellhorn, Henry Vives i Santa Eulàlia, Josep, 1963- |
Keywords: | Equacions en derivades parcials Processos estocàstics Teoria de jocs Distribució (Teoria de la probabilitat) Partial differential equations Stochastic processes Game theory Distribution (Probability theory) |
Issue Date: | Feb-2020 |
Publisher: | Elsevier B.V. |
Abstract: | In this paper we obtain a Dyson type formula for integrable functionals of a pure jump Lévy process. We represent the conditional expectation of a $\mathscr{F}_T$-measurable random variable $F$ at a time $t \leq T$ as an exponential formula involving Malliavin derivatives evaluated along a frozen path. The series representation of this exponential formula turns out to be useful for different applications, and in particular in quantitative finance, as we show in the following examples: the first one is the pricing of options in the Poisson-Black-Scholes model; the second one is the pricing of discount bonds in the Lévy quadratic model. We also obtain, for the conditional expectation of a function of a finite number of the process values, a backward Taylor expansion, that turns out to be useful for numerical calculations. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1016/j.spa.2019.03.019 |
It is part of: | Stochastic Processes and their Applications, 2020, vol. 130, num. 2, p. 824-844 |
URI: | http://hdl.handle.net/2445/193773 |
Related resource: | https://doi.org/10.1016/j.spa.2019.03.019 |
ISSN: | 0304-4149 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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