Work

On One-dimensional Stochastic Differential Equations Involving the Maximum Process

Year: 2009

Type: article

Abstract: We prove existence and pathwise uniqueness results for four different types of stochastic differential equations (SDEs) perturbed by the past maximum process and/or the local time at zero. Along the first three studies, the coefficients are no longer Lipschitz. The first type is the equation [Formula: see text] The second type is the equation [Formula: see text] The third type is the equation [Formula: see text] We end the paper by establishing the existence of strong solution and pathwise uniqueness, under Lipschitz condition, for the SDE [Formula: see text]

Source: Stochastics and Dynamics

DOI: 10.1142/s0219493709002671

Authors: R. BELFADLI, S. HAMADÈNE, Y. OUKNINE

Institutions: Cadi Ayyad University, Le Mans Université, Hassan II Academy of Science and Technology

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

OpenAlex ID: W2019898665

FWCI: 1.123

Cites: 16

Cited by: 19

Related to: 10