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 Management Department of Fondiaria-Sai S.p.A.. I present a short review of the deterministic and stochastic claims reserving methods currently applied in practice and I develop a (standard) Over-Dispersed Poisson (ODP) Bayesian model for the estimation of the Outstanding Loss Liabilities (OLLs) of a line of business (LoB). I present the model, I illustrate the theoretical foundations of the MCMC (Markov Chain Monte Carlo) method and the Metropolis-Hastings algorithm used in order to generate the non-standard posterior distributions. I apply the model to the Motor Third Party Liabil- ity LoB of Fondiaria-Sai S.p.A.. Moreover, I explore the problem of computing the prudential reserve level of a multi-line non-life insurance company. In the second chapter, then, I present a full Bayesian model for assessing the reserve requirement of multiline Non-Life insurance companies. The model combines the Bayesian approach for the estimation of marginal distribution for the single Lines of Business and a Bayesian copula procedure for their aggregation. First, I consider standard copula aggregation for different copula choices. Second, I present the Bayesian copula technique. Up to my knowledge, this approach is totally new to stochastic claims reserving. The model allows to "mix" own-assessments of dependence between LoBs at a company level and market wide estimates. I present an application to an Italian multi-line insurance company and compare the results obtained aggregating using standard copulas and a Bayesian Gaussian copula. In the second part of my Dissertation I propose a theoretical model that studies optimal capital and organizational structure choices of financial groups which incorporate two or more business units. The group faces a VaR-type regulatory capital requirement. Financial conglomerates incorporate activities in different sectors either into a unique integrated entity, into legally separated divisions or in ownership-linked holding company/subsidiary structures. I model these different arrangements in a structural framework through different coinsurance links between units in the form of conditional guarantees issued by equityholders of a firm towards the debtholders of a unit of the same group. I study the effects of the use of such guarantees on optimal capital structural and organizational form choices. I calibrate model parameters to observed financial institutions' characteristics. I study how the capital is optimally held, the costs and benefits of limiting undercapitalization in some units and I address the issues of diversification at the holding's level and regulatory capital arbitrage. The last part of my Ph.D. Dissertation studies the hedging problem of life insurance policies, when the mortality rate is stochastic. The field developed recently, adapting well-established techniques widely used in finance to describe the evolution of rates of mortality. The chapter is joint work with my supervisor, prof. Elisa Luciano and Elena Vigna. It studies the hedging problem of life insurance policies, when the mortality and interest rates are stochastic. We focus primarily on stochastic mortality. We represent death arrival as the first jump time of a doubly stochastic process, i.e. a jump process with stochastic intensity. We propose a Delta-Gamma Hedging technique for mortality risk in this context. The risk factor against which to hedge is the difference between the actual mortality intensity in the future and its "forecast" today, the instantaneous forward intensity. We specialize the hedging technique first to the case in which survival intensities are affine, then to Ornstein-Uhlenbeck and Feller processes, providing actuarial justifications for this restriction. We show that, without imposing no arbitrage, we can get equivalent probability measures under which the HJM condition for no arbitrage is satisfied. Last, we extend our results to the presence of both interest rate and mortality risk, when the forward interest rate follows a constant-parameter Hull and White process. We provide a UK calibrated example of Delta and Gamma Hedging of both mortality and interest rate risk.
| Identifer | oai:union.ndltd.org:CCSD/oai:tel.archives-ouvertes.fr:tel-00804585 |
| Date | 25 March 2011 |
| Creators | Luca, Regis |
| Source Sets | CCSD theses-EN-ligne, France |
| Language | French |
| Detected Language | English |
| Type | PhD thesis |
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