Examples and Counterexamples of Cost-efficiency in Incomplete Markets
Abstract
We present a number of examples and counterexamples to illustrate the results on cost-efficiency in an incomplete market obtained in [BS24]. These examples and counterexamples do not only illustrate the results obtained in [BS24], but show the limitations of the results and the sharpness of the key assumptions. In particular, we make use of a simple 3-state model in which we are able to recover and illustrate all key results of the paper. This example also shows how our characterization of perfectly cost-efficient claims allows to solve an expected utility maximization problem in a simple incomplete market (trinomial model) and recover results from [DS06, Chapter 3], there obtained using duality.
Cite
@article{arxiv.2407.08756,
title = {Examples and Counterexamples of Cost-efficiency in Incomplete Markets},
author = {Carole Bernard and Stephan Sturm},
journal= {arXiv preprint arXiv:2407.08756},
year = {2024}
}
Comments
21 pages, 2 tables, 3 figures. This paper contains the examples and counterexamples originally contained in arXiv:2206.12511, as per request of the journal editors