Directional Stochastic Orders with an Application to Financial Mathematics

María Concepción López-Díaz, Miguel López-Díaz and Sergio Martínez-Fernández
Additional contact information
María Concepción López-Díaz: Departamento de Matemáticas, Universidad de Oviedo, E-33007 Oviedo, Spain
Miguel López-Díaz: Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, E-33007 Oviedo, Spain
Sergio Martínez-Fernández: Unidad de Auditoría de Capital & Impairments, Banco Sabadell, E-08174 Barcelona, Spain

Mathematics, 2021, vol. 9, issue 4, 1-11

Abstract: Relevant integral stochastic orders share a common mathematical model, they are defined by generators which are made up of increasing functions on appropriate directions. Motivated by the aim to provide a unified study of those orders, we introduce a new class of integral stochastic orders whose generators are composed of functions that are increasing on the directions of a finite number of vectors. These orders will be called directional stochastic orders. Such stochastic orders are studied in depth. In that analysis, the conical combinations of vectors in those finite subsets play a relevant role. It is proved that directional stochastic orders are generated by non-stochastic pre-orders and the class of their preserving mappings. Geometrical characterizations of directional stochastic orders are developed. Those characterizations depend on the existence of non-trivial subspaces contained in the set of conical combinations. An application of directional stochastic orders to the field of financial mathematics is developed, namely, to the comparison of investments with random cash flows.

Keywords: convex cone; investment with random cash flows; non-trivial subspace; orthogonal projection; stochastic order (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/4/380/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/4/380/ (text/html)

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:gam:jmathe:v:9:y:2021:i:4:p:380-:d:499404

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().