The paper is devoted to a connection between stochastic invariance in infinite dimensions and a consistency question of mathematical finance. We derive necessary and sufficient conditions for stochastic invariance of Nagumo’s type for stochastic equations with additive noise. They are applied to Ornstein-Uhlenbeck processes and to specific financial models. The case of evolution equations with general noise is discussed also and a comparison with recent results obtained by geometric methods is presented as well.
Questo lavoro riguarda la connessione fra l’invarianza stocastica in dimensione infinita e un problema di consistenza in finanza matematica. Vengono date condizioni necessarie e sufficienti di tipo Nagumo per l’invarianza di equazioni stocastiche con rumore additivo. Esse sono applicate a processi di Ornstein-Uhlenbeck e specifici modelli finanziari. Vengono anche discusse equazioni di evoluzione con rumore generale e viene fatto un paragone con recenti risultati ottenuti con metodi geometrici.
@article{RLIN_2000_9_11_2_67_0,
author = {Jerzy Zabczyk},
title = {Stochastic invariance and consistency of financial models},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
volume = {11},
year = {2000},
pages = {67-80},
zbl = {0978.60039},
mrnumber = {1797512},
language = {en},
url = {http://dml.mathdoc.fr/item/RLIN_2000_9_11_2_67_0}
}
Zabczyk, Jerzy. Stochastic invariance and consistency of financial models. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 11 (2000) pp. 67-80. http://gdmltest.u-ga.fr/item/RLIN_2000_9_11_2_67_0/
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