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Convergence in incomplete market models. (English) Zbl 0961.60054

This paper uses methods from nonstandard analysis to prove convergence results for incomplete financial markets. More precisely, it is shown that convergence of the underlying models in the sense of \(D^2\)-convergence as introduced by N. J. Cutland, E. Kopp and W. Willinger [Math. Finance 3, No. 2, 101-123 (1993; Zbl 0884.90022)] implies the convergence of both hedging strategies and value processes for risk-minimization. This is done for the case where a complete limit model (the Black-Scholes model) is approximated either by a sequence of multinomial models or by a sequence of direct discretizations.

MSC:

60H05 Stochastic integrals
91B28 Finance etc. (MSC2000)
28E05 Nonstandard measure theory
26E35 Nonstandard analysis

Citations:

Zbl 0884.90022
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