{"title":"Randomisation with moral hazard: a path to existence of optimal contracts","authors":"Daniel Kršek, Dylan Possamaï","doi":"arxiv-2311.13278","DOIUrl":null,"url":null,"abstract":"We study a generic principal-agent problem in continuous time on a finite\ntime horizon. We introduce a framework in which the agent is allowed to employ\nmeasure-valued controls and characterise the continuation utility as a solution\nto a specific form of a backward stochastic differential equation driven by a\nmartingale measure. We leverage this characterisation to prove that, under\nappropriate conditions, an optimal solution to the principal's problem exists,\neven when constraints on the contract are imposed. In doing so, we employ\ncompactification techniques and, as a result, circumvent the typical challenge\nof showing well-posedness for a degenerate partial differential equation with\npotential boundary conditions, where regularity problems often arise.","PeriodicalId":501487,"journal":{"name":"arXiv - QuantFin - Economics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Economics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2311.13278","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 study a generic principal-agent problem in continuous time on a finite
time horizon. We introduce a framework in which the agent is allowed to employ
measure-valued controls and characterise the continuation utility as a solution
to a specific form of a backward stochastic differential equation driven by a
martingale measure. We leverage this characterisation to prove that, under
appropriate conditions, an optimal solution to the principal's problem exists,
even when constraints on the contract are imposed. In doing so, we employ
compactification techniques and, as a result, circumvent the typical challenge
of showing well-posedness for a degenerate partial differential equation with
potential boundary conditions, where regularity problems often arise.