On the stochastic integral representation of Brownian functionals-Reference-Cited by-同舟云学术

On the stochastic integral representation of Brownian functionals

Published:2023-03-02 Issue:3 Volume:30 Page:417-424
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Namgalauri Ekaterine¹,Purtukhia Omar²

Affiliation:

1. Department of Mathematics , Ivane Javakhishvili Tbilisi State University , 13 University Str. , Tbilisi 0186 , Georgia

2. Department of Mathematics , Ivane Javakhishvili Tbilisi State University , 13 University Str., 0186; and A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University, 2 Merab Aleksidze II Lane , Tbilisi 0193 , Georgia

Abstract

Abstract In this paper, we study the question of representing one class of Brownian functionals as a stochastic Itô integral with an explicit form of the integrand. The considered class of functionals also includes functionals that are not smooth in the sense of Malliavin, to which both the well-known Clark–Ocone formula (1984) and its generalization, the Glonti–Purtukhia formula (2017), are inapplicable.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2023-2001/pdf

Reference21 articles.

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4. O. Glonti and O. Purtukhia, Hedging of one european option of integral type in Black–Scholes model, Int. J. Eng. Innov. Technol. 4 (2014), no. 5, 51–61.

5. O. A. Glonti and O. G. Purtukhiya, On an integral representation of a Brownian functional (in Russian), Teor. Veroyatn. Primen. 61 (2016), no. 1, 158-164