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Stability and
asymptotic analysis of the Föllmer–Schweizer decomposition on
a finite probability space
Sarah Boese, Tracy Cui, Samuel Johnston, Sylvie Vega-Molino and Oleksii Mostovyi |
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Vol. 13 (2020), No. 4, 607–623
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Abstract |
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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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Keywords
Föllmer–Schweizer decomposition, simultaneous perturbations
of the drift and volatility, asymptotic analysis, stability
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Mathematical Subject Classification 2010
Primary: 60G07, 93E20, 91G10, 91G20, 90C31
Secondary: 60H30, 93E24
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Milestones
Received: 11 January 2020
Accepted: 23 May 2020
Published: 20 November 2020
Communicated by Jonathon Peterson
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Authors |
| Sarah Boese | |
| Vassar College Poughkeepsie, NY United States |
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| Tracy Cui | |
| Carnegie Mellon University Pittsburgh, PA United States |
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| Samuel Johnston | |
| Willamette University Salelm, OR United States |
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| Sylvie Vega-Molino | |
| Department of Mathematics University of Connecticut Storrs, CT United States |
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| Oleksii Mostovyi | |
| Department of Mathematics University of Connecticut Storrs, CT United States |
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| © 2020 MSP (Mathematical Sciences Publishers). |
