Multivariate Risk Processes with Interacting Intensities
نویسندگان
چکیده
The classical models in risk theory consider a single type of claims. In the insurance business, however, several business lines with separate claim arrival processes appear naturally, and the individual claim processes may not be independent. We introduce a new class of models for such situations, where the underlying counting process is a multivariate continuous time Markov chain of pure birth type and the dependency of the components arises from the fact that the birth rate for a specific claim type may depend on the number of claims in the other component processes. Under certain conditions we obtain a fluid limit, i.e. a functional law of large numbers for these processes. We also investigate the consequences of such results for questions of interest in insurance applications. Several specific subclasses of the general model are discussed in detail and the Cramér asymptotics of the ruin probabilities are derived in particular cases.
منابع مشابه
Analysis of Dependency Structure of Default Processes Based on Bayesian Copula
One of the main problems in credit risk management is the correlated default. In large portfolios, computing the default dependencies among issuers is an essential part in quantifying the portfolio's credit. The most important problems related to credit risk management are understanding the complex dependence structure of the associated variables and lacking the data. This paper aims at introdu...
متن کاملبررسی میزان مواجهه شغلی با پرتوهای غیریونساز و اثربخشی وسایل حفاظت فردی در انواع جوشکاری قوس الکتریکی متداول
Introduction: Welding is considered to be one of the main sources of occupational exposure to non ionizing radiations. The present study was conducted to examine the rate of occupational exposure to non-ionizing radiation in common welding processes. Materials and Methods: In the present descriptive analytical study, occupational exposure to different types of non-ionizing radiations in...
متن کاملCOVARIANCE MATRIX OF MULTIVARIATE REWARD PROCESSES WITH NONLINEAR REWARD FUNCTIONS
Multivariate reward processes with reward functions of constant rates, defined on a semi-Markov process, first were studied by Masuda and Sumita, 1991. Reward processes with nonlinear reward functions were introduced in Soltani, 1996. In this work we study a multivariate process , , where are reward processes with nonlinear reward functions respectively. The Laplace transform of the covar...
متن کاملSurvival Measures and Interacting Intensity Model: with Applications in Guaranteed Debt Pricing
This paper studies survival measures in credit risk models. Survival measure, which was first introduced by Schönbucher [12] in the framework of defaultable LMM, has the advantage of eliminating default indicator variable directly from the expectation by absorbing it into Randon-Nikodym density process. Survival measure approach was further extended by Collin-Duresne [4] to avoid calculating a ...
متن کامل