Simple view
Full metadata view
Authors
Statistics
On the parabolic equation for portfolio problems
We consider a semilinear equation linked to the finite horizon consumption-investment problem under stochastic factor framework, prove it admits a classical solution and provide all obligatory estimates to successfully apply a verification reasoning. The paper covers the standard time additive utility, as well as the recursive utility framework. We extend existing results by considering more general factor dynamics including a nontrivial diffusion part and a stochastic correlation between assets and factors. In addition, this is the first paper which compromise many other optimization problems in finance, for example those related to the indifference pricing or the quadratic hedging problem. The extension of the result to the stochastic differential utility and robust portfolio optimization is provided as well. The essence of our paper lays in using improved stochastic methods to prove gradient estimates for suitable HJB equations with restricted control space.
cris.lastimport.scopus | 2024-04-07T17:48:59Z | |
dc.abstract.en | We consider a semilinear equation linked to the finite horizon consumption-investment problem under stochastic factor framework, prove it admits a classical solution and provide all obligatory estimates to successfully apply a verification reasoning. The paper covers the standard time additive utility, as well as the recursive utility framework. We extend existing results by considering more general factor dynamics including a nontrivial diffusion part and a stochastic correlation between assets and factors. In addition, this is the first paper which compromise many other optimization problems in finance, for example those related to the indifference pricing or the quadratic hedging problem. The extension of the result to the stochastic differential utility and robust portfolio optimization is provided as well. The essence of our paper lays in using improved stochastic methods to prove gradient estimates for suitable HJB equations with restricted control space. | pl |
dc.affiliation | Wydział Matematyki i Informatyki : Instytut Matematyki | pl |
dc.contributor.author | Zawisza, Dariusz - 147964 | pl |
dc.date.accessioned | 2021-03-28T19:59:03Z | |
dc.date.available | 2021-03-28T19:59:03Z | |
dc.date.issued | 2020 | pl |
dc.date.openaccess | 0 | |
dc.description.accesstime | w momencie opublikowania | |
dc.description.physical | 287-302 | pl |
dc.description.version | ostateczna wersja wydawcy | |
dc.description.volume | 122 | pl |
dc.identifier.doi | 10.4064/bc122-16 | pl |
dc.identifier.eissn | 1730-6299 | pl |
dc.identifier.issn | 0137-6934 | pl |
dc.identifier.project | ROD UJ / O | pl |
dc.identifier.uri | https://ruj.uj.edu.pl/xmlui/handle/item/268213 | |
dc.language | eng | pl |
dc.language.container | eng | pl |
dc.rights | Dodaję tylko opis bibliograficzny | * |
dc.rights.licence | OTHER | |
dc.rights.uri | * | |
dc.share.type | otwarte czasopismo | |
dc.subtype | Article | pl |
dc.title | On the parabolic equation for portfolio problems | pl |
dc.title.journal | Banach Center Publications | pl |
dc.type | JournalArticle | pl |
dspace.entity.type | Publication |