Essays on modeling, hedging and pricing of insurance and financial products

Cette thèse est composée de trois articles abordant différentes problématiques en relation avec la modélisation, la couverture et la tarification des risques d’assurance et financiers. “A general class of distortion operators for pricing contingent claims with applications to CAT bonds” est un projet présentant une méthode générale pour dériver des opérateurs de distorsion compatibles avec la valorisation sans arbitrage. Ce travail offre également une nouvelle classe simple d’opérateurs de distorsion afin d’expliquer les primes observées dans le marché des obligations catastrophes. “Local hedging of variable annuities in the presence of basis risk” est un travail dans lequel une méthode de couverture des rentes variables en présence de risque de base est développée. La méthode de couverture proposée bénéficie d’une exposition plus élevée au risque de marché et d’une diversification temporelle du risque pour obtenir un rendement excédentaire et faciliter l’accumulation de capital. “Option pricing under regime-switching models : Novel approaches removing path-dependence” est un projet dans lequel diverses mesures neutres au risque sont construites pour les modèles à changement de régime de manière à générer des processus de prix d’option qui ne présentent pas de dépendance au chemin, en plus de satisfaire d’autres propriétés jugées intuitives et souhaitables.This thesis is composed of three papers addressing different issues in relation to the modeling, hedging and pricing of insurance and financial risks. “A general class of distortion operators for pricing contingent claims with applications to CAT bonds” is a project presenting a general method for deriving probability distortion operators consistent with arbitrage-free pricing. This work also offers a simple novel class of distortions operators for explaining catastrophe (CAT) bond spreads. “Local hedging of variable annuities in the presence of basis risk” is a work in which a method to hedge variable annuities in the presence of basis risk is developed. The proposed hedging scheme benefits from a higher exposure to equity risk and from time diversification of risk to earn excess return and facilitate the accumulation of capital. “Option pricing under regime-switching models: Novel approaches removing path-dependence” is a project in which various risk-neutral measures for hidden regime-switching models are constructed in such a way that they generate option price processes which do not exhibit path-dependence in addition to satisfy other properties deemed intuitive and desirable

2D growth processes: SLE and Loewner chains

This review provides an introduction to two dimensional growth processes. Although it covers a variety processes such as diffusion limited aggregation, it is mostly devoted to a detailed presentation of stochastic Schramm-Loewner evolutions (SLE) which are Markov processes describing interfaces in 2D critical systems. It starts with an informal discussion, using numerical simulations, of various examples of 2D growth processes and their connections with statistical mechanics. SLE is then introduced and Schramm's argument mapping conformally invariant interfaces to SLE is explained. A substantial part of the review is devoted to reveal the deep connections between statistical mechanics and processes, and more specifically to the present context, between 2D critical systems and SLE. Some of the SLE remarkable properties are explained, as well as the tools for computing with SLE. This review has been written with the aim of filling the gap between the mathematical and the physical literatures on the subject.Comment: A review on Stochastic Loewner evolutions for Physics Reports, 172 pages, low quality figures, better quality figures upon request to the authors, comments welcom