OU, Vasicek, CIR ve Hull-White Modellerine Aktüeryal Uygulamaları Üzerinden Kısa Bir Bakış

Öz

Amaç: Orntein-Uhlenbeck (OU), Vasicek, Cox-Ingersoll-Ross (CIR) ve Hull-White afin süreçleri, önemli özelliklerine kısaca değinilerek ele alınmıştır. Bu makalenin temel amacı söz konusu afin süreçlerin, farklı stokastik modeller ve matematiksel metotların kullanıldığı altı yakın dönem aktüeryal uygulamasını tartışmaktır.
Sonuç ve Katkılar: Bu uygulamalar, bir yandan söz konusu afin süreçlerin modelleme sürecine nasıl dahil edildiğini göstermekte, diğer yandan ise matematiksel hesaplamalar/veri analizi yoluyla bu afin süreçleri kullanmanın avantajları hakkında fikir vermektedir.

Anahtar Kelimeler

• Ornstein-Uhlenbeck modeli
• Vasicek modeli
• Cox-Ingersoll-Ross modeli
• Hull-White modeli.

A Brief Look at OU, Vasicek, CIR and Hull-White Models Through Their Actuarial Applications

Abstract

Aim: A brief overview of the affine processes, namely the Orntein-Uhlenbeck (OU) process, the Vasicek process, the Cox-Ingersoll-Ross (CIR) process and the Hull-White process, is presented through their important features. The main purpose of this paper is to discuss six very recent actuarial applications of these affine processes that focus on different problems with different stochastic models and different mathematical methods.
Conclusion and Contributions: On one hand, these applications show how to incorporate the corresponding affine processes into the modelling framework. On the one hand they give an insight about the advantages of using these affine processes through mathematical calculations/data analysis.

Keywords

• Ornstein-Uhlenbeck model
• Vasicek model
• Cox-Ingersoll-Ross model
• Hull-White model.

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