TL;DR
This paper surveys stochastic calculus tools for Bernoulli processes, including chaos representation, Clark formula, and applications to option hedging, highlighting recent advances in discrete-time stochastic analysis.
Contribution
It introduces a comprehensive overview of discrete-time chaotic calculus for Bernoulli processes, emphasizing new covariance identities and inequalities for financial applications.
Findings
Derived covariance identities and functional inequalities.
Applied stochastic calculus to option hedging strategies.
Extended chaos representation to discrete Bernoulli sequences.
Abstract
These notes survey some aspects of discrete-time chaotic calculus and its applications, based on the chaos representation property for i.i.d. sequences of random variables. The topics covered include the Clark formula and predictable representation, anticipating calculus, covariance identities and functional inequalities (such as deviation and logarithmic Sobolev inequalities), and an application to option hedging in discrete time.
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