A change of variable formula with applications to multi-dimensional optimal stopping problems

Abstract

We derive a change of variable formula for $C^1$ functions $U:{\mathbb{R}}_{+}\times {\mathbb{R}}^m\to \mathbb{R}$ whose second order spatial derivatives may explode and not be integrable in the neighbourhood of a surface $b:{\mathbb{R}}_{+}\times {\mathbb{R}}^{m-1}\to \mathbb{R}$ that splits the state space into two sets $\cC$ and $\cD$. The formula is tailored for applications in problems of optimal stopping where it is generally very hard to control the second order derivatives of the value function near the optimal stopping boundary. Differently to other existing papers on similar topics we only require that the surface $b$ be monotonic in each variable and we formally obtain the same expression as the classical Itô's formula.

26 pages; final version accepted for publication

References in corpus (3)

• The American put with finite-time maturity and stochastic interest rate
• Change of Variables with Local Time on Surfaces for Jump Processes
• The Local Time-Space Integral and Stochastic Differential Equations

Cited by in corpus (2)

• The American put with finite-time maturity and stochastic interest rate
• Weak equilibria for time-inconsistent control: with applications to investment-withdrawal decisions