Three Essays in Finance and Actuarial Science

Doctoral thesis French OPEN
Luca , Regis;
(2011)
  • Publisher: HAL CCSD
  • Subject: stochastic claims reserving | [ SHS.ECO ] Humanities and Social Sciences/Economies and finances | longevity risk | financial conglomerates | [SHS.ECO] Humanities and Social Sciences/Economies and finances

This thesis is constituted of three chapters. he first part of my Ph.D. dissertation develops a Bayesian stochastic model for computing the reserves of a non-life insurance company. The first chapter is the product of my research experience as an intern at the Risk Mana... View more
  • References (21)
    21 references, page 1 of 3

    1 A Bayesian stochastic reserving model 7 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Deterministic models . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1 Fisher Lange method . . . . . . . . . . . . . . . . . . . 9 1.2.2 Chain Ladder method . . . . . . . . . . . . . . . . . . 9 1.2.3 Towards a Bayesian perspective: the Bornhuetter-Ferguson method . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Stochastic models for claims reserving . . . . . . . . . . . . . . 11 1.3.1 ODP model and GLM theory . . . . . . . . . . . . . . 12 1.3.2 Obtaining full predictive distributions by simulation . . 13 1.4 Bayesian models and Markov Chain Monte Carlo methods . . 15 1.5 An ODP Bayesian model for claims reserving . . . . . . . . . 18 1.5.1 Link with GLM theory and CL parameters . . . . . . . 21 1.5.2 Multivariate normal priors . . . . . . . . . . . . . . . . 21 1.5.3 Gamma priors . . . . . . . . . . . . . . . . . . . . . . . 23 1.6 Applying the model in practice . . . . . . . . . . . . . . . . . 26 1.6.1 Tests of convergence to the prior and to the chain ladder estimates . . . . . . . . . . . . . . . . . . . . . . . 26 1.6.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.7 Conclusions and further possible model extensions . . . . . . . 33 1.8 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

    2 Bayesian Copulas for Claims Reserving 37 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.2 A Bayesian approach for computing Lob's reserves . . . . . . . 39 2.3 A copula approach to aggregate across LoBs . . . . . . . . . . 40 2.3.1 Copulas . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.3.2 Applying copulas to claims reserving . . . . . . . . . . 43 2.4 A Bayesian copula approach . . . . . . . . . . . . . . . . . . . 44 2.4.1 Bayesian Gaussian copula . . . . . . . . . . . . . . . . 45

    3 Financial Conglomerates 63 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

    3.2 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . 65

    3.3 Financial Groups and their supervision . . . . . . . . . . . . . 67 3.3.1 Financial conglomerates and coinsurance . . . . . . . . 67 3.3.2 The supervision of nancial groups . . . . . . . . . . . 68

    3.4 Modelling nancial conglomerates . . . . . . . . . . . . . . . . 69 3.4.1 Basic set up: the stand alone rm and the HG . . . . . 69 3.4.2 Integrated conglomerates . . . . . . . . . . . . . . . . . 74 3.4.3 Holding/Subsidiary structures . . . . . . . . . . . . . . 76

    3.5 Numerical Analysis: HG and IC . . . . . . . . . . . . . . . . 80 3.5.1 The Stand Alone constrained rm case: calibration . . 80 3.5.2 Integrated conglomerates . . . . . . . . . . . . . . . . . 81

    3.6 Numerical Analysis: HS . . . . . . . . . . . . . . . . . . . . . 84 3.6.1 Consolidated Supervision . . . . . . . . . . . . . . . . . 84 3.6.2 Regulating subsidiaries . . . . . . . . . . . . . . . . . . 86 3.6.3 HCM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.6.4 Regulatory arbitrage in units subject to di erent capital requirements . . . . . . . . . . . . . . . . . . . . . 89

    3.7 Concluding comments . . . . . . . . . . . . . . . . . . . . . . 90

    3.8 Appendix A - Stand Alone Maximization Problem . . . . . . . 91

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