Jin, SixianSchellhorn, HenryVives i Santa Eulàlia, Josep, 1963-2023-02-172023-02-172020-020304-4149https://hdl.handle.net/2445/193773In 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.21 p.application/pdfengcc-by-nc-nd (c) Elsevier B.V., 2020https://creativecommons.org/licenses/by-nc-nd/4.0/Equacions en derivades parcialsProcessos estocàsticsTeoria de jocsDistribució (Teoria de la probabilitat)Partial differential equationsStochastic processesGame theoryDistribution (Probability theory)info:eu-repo/semantics/article6981792023-02-17info:eu-repo/semantics/openAccess