# On perpetual American options in a multidimensional Black-Scholes model

## TL;DR

This paper develops a comprehensive framework for pricing perpetual American options on multiple dividend-paying assets within a multidimensional Black-Scholes model, using probabilistic and analytical methods.

## Contribution

It introduces a probabilistic characterization via reflected BSDEs and an analytical approach through obstacle problems for this complex setting.

## Key findings

- Probabilistic representation of option prices using reflected BSDEs.
- Analytical characterization through obstacle problems.
- Explicit early exercise premium formula.

## Abstract

We consider the problem of pricing perpetual American options written on dividend-paying assets whose price dynamics follow a multidimensional Black and Scholes model. For convex Lipschitz continuous reward functions, we give a probabilistic characterization of the fair price in terms of a reflected BSDE, and an analytical one in terms of an obstacle problem. We also provide the early exercise premium formula.