On a capital allocation by minimization of some risk indicators
Tóm tắt
European insurance sector will soon be faced with the application of the Solvency 2 regulation norms. It will create a real change in the risk management of insurance practices. The ORSA (Own Risk and Solvency Assessment) approach of the second pillar makes the capital allocation an important exercise for all insurers, especially when it comes to groups. Considering multi-branches firms, a capital allocation has to be based on multivariate risk modeling. Several allocation methods are present in the actuarial literature and insurance practices. In this paper, we focus on a risk allocation method. By minimizing some of the multivariate risk indicators, we study the coherence of the risk allocation using an axiomatic approach. Furthermore, we discuss what can be the best allocation choice for an insurance group.
Tài liệu tham khảo
citation_journal_title=Math Finance; citation_title=Coherent measures of risk; citation_author=P Artzner, F Delbaen, J-M Eber, D Heath; citation_volume=9; citation_issue=3; citation_publication_date=1999; citation_pages=203-228; citation_doi=10.1111/1467-9965.00068; citation_id=CR1
Balog D (2011) Capital allocation in financial institutions: the Euler method. Iehas discussion papers, Institute of Economics, Hungarian Academy of Sciences, June 2011
Bellini F, Bignozzi V (2013) Elicitable risk measures. Available at SSRN 2334746:
citation_journal_title=Econometrica; citation_title=Equilibrium in a reinsurance market; citation_author=K Borch; citation_volume=30; citation_publication_date=1962; citation_pages=424-444; citation_doi=10.2307/1909887; citation_id=CR4
Brunnermeier MK, Cheridito P (2014) Measuring and allocating systemic risk. Available at SSRN 2372472:
citation_journal_title=Insur Math Econ; citation_title=Coherent risk measures, coherent capital allocations and the gradient allocation principle; citation_author=A Buch, G Dorfleitner; citation_volume=42; citation_issue=1; citation_publication_date=2008; citation_pages=235-242; citation_doi=10.1016/j.insmatheco.2007.02.006; citation_id=CR6
citation_journal_title=J Bank Finance; citation_title=Risk capital allocation for rorac optimization; citation_author=A Buch, G Dorfleitner, M Wimmer; citation_volume=35; citation_issue=11; citation_publication_date=2011; citation_pages=3001-3009; citation_doi=10.1016/j.jbankfin.2011.04.001; citation_id=CR7
citation_journal_title=J Multivar Anal; citation_title=Dependence properties and bounds for ruin probabilities in multivariate compound risk models; citation_author=J Cai, H Li; citation_volume=98; citation_issue=4; citation_publication_date=2007; citation_pages=757-773; citation_doi=10.1016/j.jmva.2006.06.004; citation_id=CR8
Cénac P, Loisel S, Maume-Deschamps V, Prieur C (2014) Risk indicators with several lines of business: comparison, asymptotic behavior and applications to optimal reserve allocation. Annales de l’ISUP, 58(3)
citation_journal_title=Stat Risk Model; citation_title=Some multivariate risk indicators: minimization by using a Kiefer–Wolfowitz approach to the mirror stochastic algorithm; citation_author=P Cénac, V Maume-Deschamps, C Prieur; citation_volume=29; citation_issue=1; citation_publication_date=2012; citation_pages=47-71; citation_doi=10.1524/strm.2012.1069; citation_id=CR10
citation_journal_title=J Risk; citation_title=Coherent allocation of risk capital; citation_author=M Denault; citation_volume=4; citation_publication_date=2001; citation_pages=1-34; citation_doi=10.1080/136698701455997; citation_id=CR11
citation_journal_title=J Risk Insur; citation_title=Optimal capital allocation principles; citation_author=J Dhaene, EA Valdez, A Tsanakas, S Vanduffel; citation_volume=79; citation_issue=1; citation_publication_date=2012; citation_pages=1-28; citation_doi=10.1111/j.1539-6975.2011.01408.x; citation_id=CR12
citation_journal_title=Insur Math Econ; citation_title=Risk capital allocation by coherent risk measures based on one-sided moments; citation_author=T Fischer; citation_volume=32; citation_issue=1; citation_publication_date=2003; citation_pages=135-146; citation_doi=10.1016/S0167-6687(02)00209-3; citation_id=CR13
citation_journal_title=Math Intell; citation_title=Stochastic finance. An introduction in discrete time; citation_author=H Föllmer, A Schied, TJ Lyons; citation_volume=26; citation_issue=4; citation_publication_date=2004; citation_pages=67-68; citation_doi=10.1007/BF02985423; citation_id=CR14
Fréchet M (1951) Sur les tableaux de corrélation dont les marges sont données. Annales de l’université de Lyon, Section.A, Series 3, (14):53–77
citation_journal_title=J Am Stat Assoc; citation_title=Making and evaluating point forecasts; citation_author=T Gneiting; citation_volume=106; citation_issue=494; citation_publication_date=2011; citation_pages=746-762; citation_doi=10.1198/jasa.2011.r10138; citation_id=CR16
citation_journal_title=SIAM J Finance Math; citation_title=Duality for set-valued measures of risk; citation_author=AH Hamel, F Heyde; citation_volume=1; citation_issue=1; citation_publication_date=2010; citation_pages=66-95; citation_doi=10.1137/080743494; citation_id=CR17
citation_journal_title=Schriften des mathematischen Instituts und des Instituts für angewandte Mathematik der Universität Berlin; citation_title=Maßstabinvariante Korrelationstheorie; citation_author=W Hoeffding; citation_volume=5; citation_publication_date=1940; citation_pages=179-233; citation_id=CR18
citation_journal_title=Finance Stoch; citation_title=Vector-valued coherent risk measures; citation_author=E Jouini, M Meddeb, N Touzi; citation_volume=8; citation_issue=4; citation_publication_date=2004; citation_pages=531-552; citation_doi=10.1007/s00780-004-0127-6; citation_id=CR19
citation_journal_title=Quant Finance; citation_title=An axiomatic characterization of capital allocations of coherent risk measures; citation_author=M Kalkbrener; citation_volume=9; citation_issue=8; citation_publication_date=2009; citation_pages=961-965; citation_doi=10.1080/14697680902814266; citation_id=CR20
Maume-Deschamps V, Rullière D, Said K (2015) Impact of dependence on some multivariate risk indicators. arXiv preprint
arXiv:1507.01175
Shaked M, Shanthikumar JG (2007) Stochastic orders. Springer Series in Statistics
citation_journal_title=Workshop Conf Proc; citation_title=Elicitation and identification of properties; citation_author=I Steinwart, C Pasin, RC Williamson, S Zhang; citation_volume=34; citation_publication_date=2014; citation_pages=1-45; citation_id=CR23
Tasche D (2004) Allocating portfolio economic capital to sub-portfolios. In Economic capital: a practitioner guide, Risk Books, pp 275–302
Tasche D (2007) Euler allocation: theory and practice. Technical Report
arXiv:0708.2542
Tasche D (2008) Capital allocation to business units and sub-portfolios: the Euler principle. Papers 0708.2542,
arXiv.org
citation_journal_title=J Risk Insur; citation_title=An economic approach to capital allocation; citation_author=G Zanjani; citation_volume=77; citation_issue=3; citation_publication_date=2010; citation_pages=523-549; citation_id=CR27
Ziegel JF. Coherence and elicitability. arXiv preprint
arXiv:1303.1690