Aggregate Risk Model and Risk Measure-Based Risk Allocation

Abstract

Abstract In actuarial modeling, aggregate risk is known as more attractive rather than individual risk. It has, however, usual difficulty in finding (the exact form of) joint probability distribution. This paper considers aggregate risk model and employ translated gamma approximation to handle such distribution function formulation. In addition, we deal with the problem of risk allocation in such model. We compute in particular risk allocation based on risk measure forecasts of Value-at-Risk (VaR) and its extensions: improved VaR and Tail VaR. Risk allocation shows the contribution of each individual risk to the aggregate. It has a constraint that the risk measure of aggregate risk is equal to the aggregate of risk measure of individual risk. Keywords: allocation methods; tail-value-at-risk; translated gamma approximation. Abstrak Risiko agregat merupakan kajian yang lebih menarik dalam pemodelan aktuaria, dibandingkan dengan risiko individu. Namun fungsi distribusi risiko agregat sulit ditentukan bentuk eksaknya. Artikel ini membahas mengenai model risiko agregat dan menggunakan metode aproksimasi Translasi Gamma untuk menentukan fungsi distribusi risiko agregat. Berdasarkan fungsi distribusi tersebut, dapat diprediksi alokasi risiko agregat. Metode alokasi risiko agregat diterapkan pada ukuran risiko Value-at-Risk (VaR) dan pengembangannya: improved VaR dan Tail-VaR. Alokasi risiko menyatakan nilai kontribusi setiap risiko individu terhadap ukuran risiko agregat. Jumlahan atau agregat dari setiap alokasi risiko individu sama dengan ukuran risiko agregat. Kata kunci: aproksimasi Translasi Gamma; alokasi risiko; Tail-Value-at-Risk.

Keywords

• allocation methods
• tail-value-at-risk
• translated gamma approximation