IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-00816894.html
   My bibliography  Save this paper

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

Author

Listed:
  • Peggy Cénac

    (IMB - Institut de Mathématiques de Bourgogne [Dijon] - UB - Université de Bourgogne - CNRS - Centre National de la Recherche Scientifique)

  • Stéphane Loisel

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • 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 - Inria Grenoble - Rhône-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)

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.

Suggested Citation

  • Peggy Cénac & Stéphane Loisel & Véronique Maume-Deschamps & Clémentine Prieur, 2014. "Risk indicators with several lines of business: comparison, asymptotic behavior and applications to optimal reserve allocation," Post-Print hal-00816894, HAL.
    • Handle: RePEc:hal:journl:hal-00816894
    Note: View the original document on HAL open archive server: https://hal.science/hal-00816894
    as

    Download full text from publisher

    File URL: https://hal.science/hal-00816894/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Albrecher, Hansjörg & Constantinescu, Corina & Loisel, Stephane, 2011. "Explicit ruin formulas for models with dependence among risks," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 265-270, March.
    2. Stéphane Loisel, 2005. "Differentiation of some functionals of risk processes and optimal reserve allocation," Post-Print hal-00397289, HAL.
    3. Stéphane Loisel, 2005. "Differentiation of functionals of risk processes and optimal reserve allocation," Post-Print hal-00397290, HAL.
    4. Goovaerts, Marc J. & Laeven, Roger J.A., 2008. "Actuarial risk measures for financial derivative pricing," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 540-547, April.
    5. Stéphane Loisel, 2005. "Differentiation of some functionals of risk processes," Post-Print hal-00157739, HAL.
    6. Jan Dhaene & Andreas Tsanakas & Emiliano A. Valdez & Steven Vanduffel, 2012. "Optimal Capital Allocation Principles," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(1), pages 1-28, March.
    7. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2010. "Decision principles derived from risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 294-302, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2015. "A risk management approach to capital allocation," Working Papers hal-01163180, HAL.
    2. Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2016. "On a capital allocation by minimizing multivariate risk indicators," Post-Print hal-01082559, HAL.
    3. Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2014. "On capital allocation by minimizing multivariate risk indicators," Working Papers hal-01082559, HAL.
    4. Cuberos A. & Masiello E. & Maume-Deschamps V., 2015. "High level quantile approximations of sums of risks," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-18, October.
    5. Véronique Maume-Deschamps & Didier Rullière & Khalil Said, 2017. "Impact of Dependence on Some Multivariate Risk Indicators," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 395-427, June.
    6. repec:hal:wpaper:hal-01171395 is not listed on IDEAS

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Loisel, Stéphane & Trufin, Julien, 2014. "Properties of a risk measure derived from the expected area in red," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 191-199.
    2. repec:hal:wpaper:hal-00816894 is not listed on IDEAS
    3. Mohamed Amine Lkabous & Jean-François Renaud, 2018. "A VaR-Type Risk Measure Derived from Cumulative Parisian Ruin for the Classical Risk Model," Risks, MDPI, vol. 6(3), pages 1-11, August.
    4. Macci, Claudio, 2008. "Large deviations for the time-integrated negative parts of some processes," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 75-83, January.
    5. G. A. Delsing & M. R. H. Mandjes & P. J. C. Spreij & E. M. M. Winands, 2018. "An optimization approach to adaptive multi-dimensional capital management," Papers 1812.08435, arXiv.org.
    6. Cénac P. & Maume-Deschamps V. & Prieur C., 2012. "Some multivariate risk indicators: Minimization by using a Kiefer–Wolfowitz approach to the mirror stochastic algorithm," Statistics & Risk Modeling, De Gruyter, vol. 29(1), pages 47-72, March.
    7. Julien Callant & Julien Trufin & Pierre Zuyderhoff, 2022. "Some Expressions of a Generalized Version of the Expected Time in the Red and the Expected Area in Red," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 595-611, June.
    8. Zhu, Jinxia & Yang, Hailiang, 2009. "On differentiability of ruin functions under Markov-modulated models," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1673-1695, May.
    9. Liu, Jingchen & Woo, Jae-Kyung, 2014. "Asymptotic analysis of risk quantities conditional on ruin for multidimensional heavy-tailed random walks," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 1-9.
    10. Romain Biard & Christophette Blanchet-Scalliet & Anne Eyraud-Loisel & Stéphane Loisel, 2013. "Impact of Climate Change on Heat Wave Risk," Risks, MDPI, vol. 1(3), pages 1-16, December.
    11. Esther Frostig & Adva Keren–Pinhasik, 2017. "Parisian ruin in the dual model with applications to the G/M/1 queue," Queueing Systems: Theory and Applications, Springer, vol. 86(3), pages 261-275, August.
    12. Major, John A., 2018. "Distortion measures and homogeneous financial derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 82-91.
    13. Florin Avram & Sooie-Hoe Loke, 2018. "On Central Branch/Reinsurance Risk Networks: Exact Results and Heuristics," Risks, MDPI, vol. 6(2), pages 1-18, April.
    14. Cossette, Hélène & Marceau, Etienne & Trufin, Julien & Zuyderhoff, Pierre, 2020. "Ruin-based risk measures in discrete-time risk models," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 246-261.
    15. Romain Biard & Stéphane Loisel & Claudio Macci & Noel Veraverbeke, 2010. "Asymptotic behavior of the finite-time expected time-integrated negative part of some risk processes and optimal reserve allocation," Post-Print hal-00372525, HAL.
    16. Lkabous, Mohamed Amine & Wang, Zijia, 2023. "On the area in the red of Lévy risk processes and related quantities," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 257-278.
    17. Romain Biard, 2013. "Asymptotic multivariate finite-time ruin probabilities with heavy-tailed claim amounts: Impact of dependence and optimal reserve allocation," Post-Print hal-00538571, HAL.
    18. Denuit, Michel & Robert, Christian Y., 2022. "Dynamic conditional mean risk sharing in the compound Poisson surplus model," LIDAM Discussion Papers ISBA 2022034, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Furman, Edward & Kye, Yisub & Su, Jianxi, 2021. "Multiplicative background risk models: Setting a course for the idiosyncratic risk factors distributed phase-type," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 153-167.
    20. Furman, Edward & Kuznetsov, Alexey & Zitikis, Ričardas, 2018. "Weighted risk capital allocations in the presence of systematic risk," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 75-81.
    21. Albrecht, Peter & Huggenberger, Markus, 2017. "The fundamental theorem of mutual insurance," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 180-188.

    More about this item

    Keywords

    risk indicators; capital allocation; dependent lines of business;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-00816894. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.