A constructive method for convex solutions of a class of nonlinear Black-Scholes equations-Reference-Cited by-同舟云学术

A constructive method for convex solutions of a class of nonlinear Black-Scholes equations

Published:2019-07-20 Issue:1 Volume:9 Page:654-664
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Abounouh Mostafa¹,Al Moatassime Hassan¹,Driouch Aicha¹²,Goubet Olivier²

Affiliation:

1. Department of Mathematics , Cadi Ayyad university, Faculty of science and technology , Av. Abdelkarim El Khattabi, Gueliz, 40000 Marrakech , Marocco , Monaco

2. LAMFA CNRS UMR 7352 , Université de Picardie Jules Verne , 33 rue Saint-Leu 80039 , Amiens Cedex , France

Abstract

Abstract In this work, we are concerned with the theoretical study of a nonlinear Black-Scholes equation resulting from market frictions. We will focus our attention on Barles and Soner’s model where the volatility is enlarged due to the presence of transaction costs. The aim of this paper is to give a constructive mathematical approach for proving the existence of convex solutions to a non degenerate fully nonlinear deterministic problem with nonlinear dependence upon the highest derivative. The existence of a strong solution to the original equation is shown by considering a monotone sequence satisfying an abstract Barenblatt equation and converging toward the solution of a limit problem.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Reference20 articles.

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3. B. Bouchard, L. Moreau and H. M. Soner, Hedging under an expected loss constraint with small transaction costs. SIAM Journal on Financial Mathematics, 7(1) (2016), pp. 508-551.

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5. E. Denis, Approximate Hedging of Contingent Claims under Transaction Costs for a more General Payoff. Applied Mathematical Finance, 17(6) (2010), pp. 491-518.

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