On the risk consistency and monotonicity of ruin theory

Assa, Hirbod and Constantinescu, Corina ORCID: 0000-0002-5219-3022 (2021) On the risk consistency and monotonicity of ruin theory European Actuarial Journal, 11 (2). pp. 709-715. ISSN 2190-9733, 2190-9741

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Abstract

Setting a proper minimum capital requirement is one of the most fundamental problems in the insurance industry. Ruin theory proposes a solution to this problem by identifying the minimum capital that a company needs to hold in order to stay solvent with a high probability. In this note we discuss the ruin theory risk consistency. More precisely we show that the ruin-consistent Value-at-Risk (VaR) is not continuous in probability, in L^p, 0 ≤ p< ∞, and in weak convergence. Furthermore, it is not a monotone measure of risk.

Item Type:	Article
Uncontrolled Keywords:	35 Commerce, Management, Tourism and Services, 3502 Banking, Finance and Investment, 4901 Applied Mathematics, 49 Mathematical Sciences, 4905 Statistics
Divisions:	Faculty of Science & Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	12 Apr 2021 07:23
Last Modified:	01 Mar 2026 10:48
DOI:	10.1007/s13385-021-00272-3
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3118792
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