On the Perpetual American Put Options for Level Dependent Volatility Models with Jumps

Abstract

We prove that the perpetual American put option price of level dependent volatility model with compound Poisson jumps is convex and is the classical solution of its associated quasi-variational inequality, that it is $C^2$ except at the stopping boundary and that it is $C^1$ everywhere (i.e. the smooth pasting condition always holds).

References in corpus (2)

• Adaptive Poisson disorder problem
• Quickest Detection for a Poisson Process with a Phase-type Change-time Distribution