Differentiation of some functionals of risk processes

Stéphane Loisel

Post-Print from HAL

Abstract: For general risk processes, the expected time-integrated negative part of the process on a fixed time interval is introduced and studied. Differentiation theorems are stated and proved. They make it possible to derive the expected value of this risk measure, and to link it with the average total time below zero studied by Dos Reis (1993) and the probability of ruin. Differentiation of other functionals of unidimensional and multidimensional risk processes with respect to the initial reserve level are carried out. Applications to ruin theory, and to the determination of the optimal allocation of the global initial reserve which minimizes one of these risk measures, illustrate the variety of application fields and the benefits deriving from an efficient and effective use of such tools.

Keywords: Ruin theory; Sample path properties; Optimal allocation; Multidimensional risk process; Risk measures (search for similar items in EconPapers)
Date: 2005-06-15
Note: View the original document on HAL open archive server: https://hal.science/hal-00157739v2
References: Add references at CitEc
Citations: View citations in EconPapers (23)

Published in Journal of Applied Probability, 2005, 42 (2), pp.379-392. ⟨10.1239/jap/1118777177⟩

Downloads: (external link)
https://hal.science/hal-00157739v2/document (application/pdf)

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:hal:journl:hal-00157739

DOI: 10.1239/jap/1118777177

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().