Lower bounds for densities of Asian type stochastic differential equations
type: Item
instance of: scholarly article
title: Lower bounds for densities of Asian type stochastic differential equations
zbMATH Open document ID: 1196.60105
author: Vlad Bally
author: Arturo Kohatsu-Higa
published in: Journal of Functional Analysis
publication date: 2010-05-17T00:00:00Z
review text: Consider the following system of stochastic differential equations, \[ X^1_t = x^1 + \int_0^t \sigma(X_s)dW_s + \int_0^t b_1(X_s)ds, \quad X^2_t = x^2 + \int_0^t b_2(X_s)ds, \quad t \in [0,T]. \] They assume that \(\sigma,b_1,b_2\) are five times differentiable and have bounded derivatives but the functions themselves do not need to be bounded. The main goal of this paper is to give lower bounds for the density \(p_T(x,y)\) of \(X_T(x)\). These type of equations are linked to the so-called Asian option set-up as the authors claims.
reviewed by: Nikolaos Halidias
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 91G80
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 91G20
zbMATH DE Number: 5708601
zbMATH Keywords: lower bounds
zbMATH Keywords: density function
zbMATH Keywords: Asian type SDE's
zbMATH Keywords: Malliavin calculus
MaRDI profile type: Publication
full work available at URL: j.jfa.2009.10.027
OpenAlex ID: W2080970984
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DOI: 10.1016/J.JFA.2009.10.027
description: scientific article; zbMATH DE number 5708601