#2242. Convergence of optimal expected utility for a sequence of binomial models

August 2026publication date
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Journal’s subject area:
Applied Mathematics;
Accounting;
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Abstract:
We consider the convergence of the solution of a discrete-time utility maximization problem for a sequence of binomial models to the Black-Scholes-Merton model for general utility functions. In the present article we show that convergence holds for the symmetric case and for negatively skewed binomial models. The proof depends on some rather fine estimates of the tail behaviors of binomial random variables. We also review some general results on the convergence of discrete models to Black-Scholes-Merton as developed in a recent monograph by D. Kreps.
Keywords:
Black-Scholes-Merton model; Cox-Ross-Rubinstein model; discrete versus continuous time; optimal expected utility

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