Convergence of Optimal Expected Utility for a Sequence of Binomial Models

Friedrich Hubalek and Walter Schachermayer

Papers from arXiv.org

Abstract: We analyze the convergence of expected utility under the approximation of the Black-Scholes model by binomial models. In a recent paper by D. Kreps and W. Schachermayer a surprising and somewhat counter-intuitive example was given: such a convergence may, in general, fail to hold true. This counterexample is based on a binomial model where the i.i.d. logarithmic one-step increments have strictly positive third moments. This is the case, when the up-tick of the log-price is larger than the down-tick. In the paper by D. Kreps and W. Schachermayer it was left as an open question how things behave in the case when the down-tick is larger than the up-tick and -- most importantly -- in the case of the symmetric binomial model where the up-tick equals the down-tick. Is there a general positive result of convergence of expected utility in this setting? In the present note we provide a positive answer to this question. It is based on some rather fine estimates of the convergence arising in the Central Limit Theorem.

Date: 2020-09
New Economics Papers: this item is included in nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://arxiv.org/pdf/2009.09751 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2009.09751

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().