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Malliavin calculus in Lévy spaces and applications to finance. (English) Zbl 1193.60075

Summary: The main goal of this paper is to generalize the results of E. Fournie et al. [Finance Stoch. 3, No. 4, 391–412 (1999; Zbl 0947.60066)] for markets generated by Lévy processes. For this reason we extend the theory of Malliavin calculus to provide the tools that are necessary for the calculation of the sensitivities, such as differentiability results for the solution of a stochastic differential equation.

MSC:

60H07 Stochastic calculus of variations and the Malliavin calculus
60G51 Processes with independent increments; Lévy processes
91G80 Financial applications of other theories

Citations:

Zbl 0947.60066
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