Set-valued risk measures as backward stochastic difference inclusions and equations

Çağın Ararat () and Zachary Feinstein ()
Additional contact information
Çağın Ararat: Bilkent University
Zachary Feinstein: Stevens Institute of Technology

Finance and Stochastics, 2021, vol. 25, issue 1, No 3, 43-76

Abstract: Abstract Scalar dynamic risk measures for univariate positions in continuous time are commonly represented via backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of set-valued functionals in the recent literature. There are two possible extensions of scalar backward stochastic differential equations for the set-valued framework: (1) backward stochastic differential inclusions, which evaluate the risk dynamics on the selectors of acceptable capital allocations; or (2) set-valued backward stochastic differential equations, which evaluate the risk dynamics on the full set of acceptable capital allocations as a singular object. In this work, the discrete-time setting is investigated with difference inclusions and difference equations in order to provide insights for such differential representations for set-valued dynamic risk measures in continuous time.

Keywords: Set-valued risk measure; Dynamic risk measure; Difference inclusion; Set-valued difference equation; Time-consistency; 26E25; 28B20; 34A60; 39A50; 46A20; 91B30 (search for similar items in EconPapers)
JEL-codes: D81 G32 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s00780-020-00445-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:finsto:v:25:y:2021:i:1:d:10.1007_s00780-020-00445-0

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

DOI: 10.1007/s00780-020-00445-0

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().