Work

On the one-sided Tanaka equation with drift

Year: 2011

Type: article

Abstract: We study questions of existence and uniqueness of weak and strong solutions for a one-sided Tanaka equation with constant drift lambda. We observe a dichotomy in terms of the values of the drift parameter: for $\lambda\leq 0$, there exists a strong solution which is pathwise unique, thus also unique in distribution; whereas for $\lambda > 0$, the equation has a unique in distribution weak solution, but no strong solution (and not even a weak solution that spends zero time at the origin). We also show that strength and pathwise uniqueness are restored to the equation via suitable ``Brownian perturbations".

Source: Electronic Communications in Probability

DOI: 10.1214/ecp.v16-1665

Authors: Ioannis Karatzas, Albert Shiryaev, Mykhaylo Shkolnikov

Institutions: Columbia University, Steklov Mathematical Institute, Stanford University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $675

Funder: National Science Foundation