Stochastic invariance and consistency of financial models

Jerzy Zabczyk

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2000)

  • Volume: 11, Issue: 2, page 67-80
  • ISSN: 1120-6330

Abstract

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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.

How to cite

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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 11.2 (2000): 67-80. <http://eudml.org/doc/252313>.

@article{Zabczyk2000,
abstract = {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.},
author = {Zabczyk, Jerzy},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Stochastic equations; Invariant sets; Forward curve; Consistency; stochastic equations; invariant sets; forward curve; consistency},
language = {eng},
month = {6},
number = {2},
pages = {67-80},
publisher = {Accademia Nazionale dei Lincei},
title = {Stochastic invariance and consistency of financial models},
url = {http://eudml.org/doc/252313},
volume = {11},
year = {2000},
}

TY - JOUR
AU - Zabczyk, Jerzy
TI - Stochastic invariance and consistency of financial models
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2000/6//
PB - Accademia Nazionale dei Lincei
VL - 11
IS - 2
SP - 67
EP - 80
AB - 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.
LA - eng
KW - Stochastic equations; Invariant sets; Forward curve; Consistency; stochastic equations; invariant sets; forward curve; consistency
UR - http://eudml.org/doc/252313
ER -

References

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