Some Expressions of a Generalized Version of the Expected Time in the Red and the Expected Area in Red

Julien Callant; Julien Trufin; Pierre Zuyderhoff

doi:10.1007/s11009-021-09915-0

Some Expressions of a Generalized Version of the Expected Time in the Red and the Expected Area in Red

Julien Callant, Julien Trufin, Pierre Zuyderhoff

Research output: Journal Publication › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, we study a generalized version of the expected time in the red and the expected area in red introduced in Loisel (2005). We derive some expressions for this risk measure both in light tailed and heavy tailed cases for general risk processes. Then, some further expressions are obtained for Lévy processes together with an upper bound in the light-tailed case and an additional result for large initial capitals in the subexponential case.

Original language	English
Pages (from-to)	595-611
Number of pages	17
Journal	Methodology and Computing in Applied Probability
Volume	24
Issue number	2
DOIs	https://doi.org/10.1007/s11009-021-09915-0
Publication status	Published - Jun 2022
Externally published	Yes

Keywords

Asymptotic behavior
Expected area in red
Expected time in the red
Lévy processes
Upper bound

ASJC Scopus subject areas

Statistics and Probability
General Mathematics

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10.1007/s11009-021-09915-0

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abstract = "In this paper, we study a generalized version of the expected time in the red and the expected area in red introduced in Loisel (2005). We derive some expressions for this risk measure both in light tailed and heavy tailed cases for general risk processes. Then, some further expressions are obtained for L{\'e}vy processes together with an upper bound in the light-tailed case and an additional result for large initial capitals in the subexponential case.",

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AU - Zuyderhoff, Pierre

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KW - Asymptotic behavior

KW - Expected area in red

KW - Expected time in the red

KW - Lévy processes

KW - Upper bound

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Some Expressions of a Generalized Version of the Expected Time in the Red and the Expected Area in Red

Abstract

Keywords

ASJC Scopus subject areas

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