Risk indicators with several lines of business: comparison, asymptotic behavior and applications to optimal reserve allocation

Peggy Cénac (), Stéphane Loisel, Véronique Maume-Deschamps () and Clémentine Prieur ()
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Peggy Cénac: IMB - Institut de Mathématiques de Bourgogne [Dijon] - UB - Université de Bourgogne - CNRS - Centre National de la Recherche Scientifique
Véronique Maume-Deschamps: ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique, PSPM - Probabilités, statistique, physique mathématique - ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique
Clémentine Prieur: MOISE - Modelling, Observations, Identification for Environmental Sciences - Centre Inria de l'Université Grenoble Alpes - Inria - Institut National de Recherche en Informatique et en Automatique - LJK - Laboratoire Jean Kuntzmann - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - CNRS - Centre National de la Recherche Scientifique - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques - INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques - CNRS - Centre National de la Recherche Scientifique

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Abstract: In a multi-dimensional risk model with dependent lines of business, we propose to allocate capital with respect to the minimization of some risk indicators. These indicators are sums of expected penalties due to the insolvency of a branch while the global reserve is either positive or negative. Explicit formulas in the case of two branches are obtained for several models independent exponential, correlated Pareto). The asymptotic behavior (as the initial capital goes to infinity) is studied. For higher dimension and several periods, no explicit expression is available. Using a stochastic algorithm, we get estimations of the allocation, compare the different allocations and study the impact of dependence.

Keywords: risk indicators; capital allocation; dependent lines of business (search for similar items in EconPapers)
Date: 2014
New Economics Papers: this item is included in nep-rmg
Note: View the original document on HAL open archive server: https://hal.science/hal-00816894v1
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Citations: View citations in EconPapers (9)

Published in Annales de l'ISUP, 2014, 58 (3), pp.3-26

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00816894

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