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2020 Stability and asymptotic analysis of the Föllmer–Schweizer decomposition on a finite probability space
Sarah Boese, Tracy Cui, Samuel Johnston, Gianmarco Molino, Oleksii Mostovyi
Involve 13(4): 607-623 (2020). DOI: 10.2140/involve.2020.13.607

Abstract

First, we consider the problem of hedging in complete binomial models. Using the discrete-time Föllmer–Schweizer decomposition, we demonstrate the equivalence of the backward induction and sequential regression approaches. Second, in incomplete trinomial models, we examine the extension of the sequential regression approach for approximation of contingent claims. Then, on a finite probability space, we investigate stability of the discrete-time Föllmer–Schweizer decomposition with respect to perturbations of the stock price dynamics and, finally, perform its asymptotic analysis under simultaneous perturbations of the drift and volatility of the underlying discounted stock price process, where we prove stability and obtain explicit formulas for the leading-order correction terms.

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Sarah Boese. Tracy Cui. Samuel Johnston. Gianmarco Molino. Oleksii Mostovyi. "Stability and asymptotic analysis of the Föllmer–Schweizer decomposition on a finite probability space." Involve 13 (4) 607 - 623, 2020. https://doi.org/10.2140/involve.2020.13.607

Information

Received: 11 January 2020; Accepted: 23 May 2020; Published: 2020
First available in Project Euclid: 22 December 2020

MathSciNet: MR4190427
Digital Object Identifier: 10.2140/involve.2020.13.607

Subjects:
Primary: 60G07, 90C31, 91G10, 91G20, 93E20
Secondary: 60H30, 93E24

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 4 • 2020
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