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Stability and asymptotic analysis of the Föllmer-Schweizer decomposition on a finite probability space. (English) Zbl 1470.60108

Summary: 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.

MSC:

60G07 General theory of stochastic processes
91G10 Portfolio theory
91G20 Derivative securities (option pricing, hedging, etc.)
93E20 Optimal stochastic control
93E24 Least squares and related methods for stochastic control systems
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References:

[1] 10.1214/105051606000000259 · Zbl 1149.91035
[2] 10.1214/105051606000000529 · Zbl 1132.91426
[3] 10.1214/aop/1176988281 · Zbl 0830.60040
[4] 10.1016/j.spa.2020.01.003 · Zbl 1443.91276
[5] 10.1214/aop/1176988611 · Zbl 0814.60041
[6] 10.1287/moor.20.1.1 · Zbl 0835.90008
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