NORBERG Ragnar

Analyzing the effect of business cycle on rating transitions has been a subject of great interest these last fifteen years, particularly due to the increasing pressure coming from regulators for stress testing. In this paper, we consider that the dynamics of rating migrations is governed by an unobserved latent factor. Under a point process filtering framework, we explain how the current state of the hidden factor can be efficiently inferred from observations of rating histories. We then adapt the classical Baum-Welsh algorithm to our setting and show how to estimate the latent factor parameters. Once calibrated, we may reveal and detect economic changes affecting the dynamics of rating migration, in real-time. To this end we adapt a filtering formula which can then be used for predicting future transition probabilities according to economic regimes without using any external covariates. We propose two filtering frameworks: a discrete and a continuous version. We demonstrate and compare the efficiency of both approaches on fictive data and on a corporate credit rating database. The methods could also be applied to retail credit loans.

The distribution of incomes of a population, the distribution of failure times of a material and the evolution of profits of life insurance contracts - studied in economics and management - are related to continuous functions belonging to the class of distribution functionals. Our thesis deals with the kernel estimation of distribution functionals with applications in economics and management sciences. In the first chapter, we propose local polynomial estimators in the i.i.d. framework of two distribution functionals, denoted LF and TF , useful to produce smooth estimators of the Lorenz curve and the scaled total time on test transform. The estimation method is described in Abdous, Berlinet and Hengartner (2003) and we prove the good asymptotic behavior of local polynomial estimators. Until then, Gastwirth (1972) and Barlow and Campo (1975) had defined piecewise continuous estimators of the Lorenz curve and the total normalized test time, which did not respect the continuity property of the initial curves. Illustrations on simulated and real data are proposed. The second chapter aims at providing local polynomial estimators in the i.i.d. framework of the successive derivatives of the distribution functionals explored in the previous chapter. Apart from the estimation of the first derivative of the TF function, which is treated using the smooth estimation of the distribution function, the estimation method employed is the local polynomial approximation of the distribution functionals detailed in Berlinet and Thomas-Agnan (2004). Various types of convergence as well as asymptotic normality are obtained, including for the density and its successive derivatives. Simulations appear and are commented. The starting point of the third chapter is the Parzen-Rosenblatt estimator (Rosenblatt (1956), Parzen (1964)) of the density. We first improve the bias of the Parzen-Rosenblatt estimator and its successive derivatives using higher order kernels (Berlinet (1993)). We then prove the new asymptotic normality conditions of these estimators. Finally, we construct an edge effect correction method for estimators of density derivatives using higher order derivatives. The last chapter focuses on the hazard rate, which unlike the two distribution functionals treated in the first chapter, is not a ratio of two linear distribution functionals. In the i.i.d. framework, the kernel estimators of the hazard rate and its successive derivatives are constructed from the kernel estimators of the density and its successive derivatives. The asymptotic normality of the first estimators is logically obtained from that of the second. We then place ourselves in the multiplicative intensity model, a more general framework encompassing censored and dependent data. We conduct the Ramlau-Hansen (1983) forward procedure to obtain good asymptotic properties of the estimators of the hazard rate and its successive derivatives and then attempt to apply the local polynomial approximation in this context. The rate of accumulation of surplus in the area of profit sharing can then be estimated nonparametrically since it depends on the transition rates (hazard rate from one state to another) of a Markov chain (Ramlau-Hansen (1991), Norberg (1999)).

No summary available.

This thesis aims at developing tools and models adapted to the study of certain spatial and networked risks. It is divided into five chapters. The first one consists in a general introduction, containing the state of the art within which the various works are included, as well as the main results obtained. Chapter 2 proposes a new multi-site precipitation generator. It is important to have models capable of producing statistically realistic precipitation series. While the models previously introduced in the literature are mainly concerned with daily precipitation, we develop an hourly model. It involves only one equation and thus introduces a dependence between occurrence and intensity, processes often considered as independent in the literature. It includes a common factor taking into account the large-scale atmospheric conditions and a multivariate autoregressive spillover term, representing the local rainfall propagation. In spite of its relative simplicity, this model reproduces very well the intensities, the durations of drought as well as the spatial dependence in the case of Northern Brittany. In Chapter 3, we propose a method for estimating max-stable processes, based on simulated likelihood techniques. Max-stable processes are very well suited to the statistical modelling of spatial extremes, but their estimation is delicate. Indeed, the multivariate density does not have an explicit form and standard estimation methods related to the likelihood cannot be applied. Under appropriate assumptions, our estimator is efficient when the number of temporal observations and the number of simulations tend to infinity. This simulation approach can be used for many classes of max-stable processes and can provide better results than current methods using composite likelihood, especially in the case where only a few time observations are available and the spatial dependence is important.

An investment strategy or portfolio is uniquely determined by an exposure process specifying the number of shares held in risky assets at any time and a cost process representing deposits into and withdrawals from the portfolio account. The strategy is a hedge of a contractual payment stream if the payments are currently deposited on/withdrawn from the portfolio account and the terminal value of the portfolio is 0 (ultimate settlement of the contractual liabilities). The purpose of the hedge is stated as an optimization criterion for the investment strategy. The purpose of the present paper is two-fold. Firstly, it reviews the core of quadratic hedging theory in a scenario where insurance risk can partly be offset by trading in available insurance-linked derivatives (e.g. catastrophe bonds or mortality bonds) and relates it to actuarial principles of premium rating and provision of reserves. Working under a martingale measure and some weak integrability conditions allows simple proofs based on orthogonal projections: quadratic hedging theory without agonizing pain. Secondly, it is pointed out that certain quadratic hedging principles lead to the same optimal exposure process but different optimal cost processes, special cases being mean-variance hedging and risk minimization. It is shown that these results are preserved if the value of the portfolio is required to coincide with a given adapted process, a case in point being the capital requirement introduced through regulatory regimes like the Basel accords and Solvency II.