{"title":"Examples and Counterexamples of Cost-efficiency in Incomplete Markets","authors":"Carole Bernard, Stephan Sturm","doi":"arxiv-2407.08756","DOIUrl":null,"url":null,"abstract":"We present a number of examples and counterexamples to illustrate the results\non cost-efficiency in an incomplete market obtained in [BS24]. These examples\nand counterexamples do not only illustrate the results obtained in [BS24], but\nshow the limitations of the results and the sharpness of the key assumptions.\nIn particular, we make use of a simple 3-state model in which we are able to\nrecover and illustrate all key results of the paper. This example also shows\nhow our characterization of perfectly cost-efficient claims allows to solve an\nexpected utility maximization problem in a simple incomplete market (trinomial\nmodel) and recover results from [DS06, Chapter 3], there obtained using\nduality.","PeriodicalId":501045,"journal":{"name":"arXiv - QuantFin - Portfolio Management","volume":"35 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Portfolio Management","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.08756","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.
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