Stochastic Analysis for Obtuse Random Walks

Uwe Franz () and Tarek Hamdi ()
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Uwe Franz: UFC
Tarek Hamdi: IPEST, Université de Carthage

Journal of Theoretical Probability, 2015, vol. 28, issue 2, 619-649

Abstract: Abstract We present a construction of the basic operators of stochastic analysis (gradient and divergence) for a class of discrete-time normal martingales called obtuse random walks. The approach is based on the chaos representation property and discrete multiple stochastic integrals. We show that these operators satisfy similar identities as in the case of the Bernoulli random walks. We prove a Clark–Ocone-type predictable representation formula, obtain two covariance identities and derive a deviation inequality. We close the exposition by an application to option hedging in discrete time.

Keywords: Obtuse random walks; Normal martingale; Stochastic integrals; Discrete time; Chaotic calculus; Option hedging; Primary 60G42; Secondary 60G50; 60H30 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10959-013-0522-z

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