Tightened Exponential Bounds for Discrete Time, Conditionally Symmetric Martingales with Bounded Jumps

TL;DR

This paper introduces new exponential bounds for discrete-time, conditionally symmetric martingales with bounded jumps, extending to sub- and supermartingales, and compares these bounds with existing ones.

Contribution

It provides novel exponential bounds for conditionally symmetric martingales with bounded jumps, including extensions to sub- and supermartingales, and offers a comparison with prior bounds.

Findings

New exponential bounds for martingales with bounded jumps

Extensions to sub- and supermartingales

Comparison with existing bounds

Abstract

This letter derives some new exponential bounds for discrete time, real valued, conditionally symmetric martingales with bounded jumps. The new bounds are extended to conditionally symmetric sub/ supermartingales, and they are compared to some existing bounds.