T-Systems and the lower Snell envelope

TL;DR

This paper investigates the lower Snell envelope in American option pricing, constructing a regular version of the process using advanced stochastic process regularization techniques.

Contribution

It introduces a method to construct a regular version of the lower Snell envelope employing T-Systems and regularization results, advancing the theoretical understanding of American options.

Findings

Constructed a regular version of the lower Snell envelope

Applied Dellacherie and Lenglart's regularization results

Enhanced theoretical framework for American option pricing

Abstract

The dynamical analysis of American options has motivated the development of robust versions of the classical Snell envelopes. The cost of superhedging an American option is characterized by the upper Snell envelope. The infimum of the arbitrage free prices is characterized by the lower Snell envelope. In this paper we focus on the lower Snell envelope. We construct a regular version of this stochastic process. To this end, we apply results due to Dellacherie and Lenglart on regularization of stochastic processes and T -Systems.