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All Journal Journal of Mathematical and Fundamental Sciences InPrime: Indonesian Journal Of Pure And Applied Mathematics Jurnal Matematika Integratif
Khreshna Syuhada
Institut Teknologi Bandung
Astronomy Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Electrical & Electronics Engineering Engineering Mathematics Mechanical Engineering Physics Transportation

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Prediction Limits for Poisson INAR(1) Process Khreshna Syuhada; Abdulhamid Alzaid; Salah Djemili
Journal of Mathematical and Fundamental Sciences Vol. 47 No. 2 (2015)
Publisher : Institute for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/j.math.fund.sci.2015.47.2.1

Abstract

We discuss the problem of deriving an estimative prediction limit as well as a simulation-based improved prediction limit for a future realization from the stationary, first-order Poisson INAR(1) process. An assessment of these limits was carried out by calculating their coverage probability, conditional on the last observation. It was found that while an estimative prediction limit may always be calculated, an improved prediction limit may not be obtained due to its discreteness and expectation to obtain a coherent prediction.
Aggregate Risk Model and Risk Measure-Based Risk Allocation Khreshna Syuhada
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 1 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2675.61 KB) | DOI: 10.15408/inprime.v2i1.14494

Abstract

AbstractIn 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. AbstrakRisiko 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.
Bounds of Adj-TVaR Prediction for Aggregate Risk Khreshna Syuhada
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 1, No 1 (2019)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2527.467 KB) | DOI: 10.15408/inprime.v1i1.12788

Abstract

In financial and insurance industries, risks may come from several sources. It is therefore important to predict future risk by using the concept of aggregate risk. Risk measure prediction plays important role in allocating capital as well as in controlling (and avoiding) worse risk. In this paper, we consider several risk measures such as Value-at-Risk (VaR), Tail VaR (TVaR) and its extension namely Adjusted TVaR (Adj-TVaR). Specifically, we perform an upper bound for such risk measure applied for aggregate risk models. The concept and property of comonotonicity and convex order are utilized to obtain such upper bound.Keywords:        Coherent property, comonotonic rv, convex order, tail property, Value-at-Risk (VaR).
Prediksi Risiko Perubahan Perilaku Nasabah Asuransi Berbasis Matriks Stokastik dan Model INAR(1) Poisson Dwi Haryanto; Khreshna I.A. Syuhada
Jurnal Matematika Integratif Vol 15, No 2: Oktober, 2019
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (400.22 KB) | DOI: 10.24198/jmi.v15.n2.23441.89

Abstract

Salah satu risiko yang mungkin dialami perusahaan asuransi adalah menurunnya pendapatan yang bersumber dari premi nasabah. Penurunan pendapatan tersebut diakibatkan karena frekuensi nasabah yang keluar lebih besar daripada frekuensi nasabah yang baru masuk (mendaftar). Oleh karena itu, perlu dilakukan kontrol terhadap pola perubahan perilaku nasabah untuk meminimalisir risiko. Pada artikel ini, dilakukan prediksi risiko dari suatu produk asuransi yaitu prediksi frekuensi pembayaran premi yang telah dilakukan nasabah atau selanjutnya disebut sebagai prediksi waktu atas loyalitas nasabah dan prediksi atas kemungkinan berkurangnya frekuensi nasabah. Prediksi waktu atas loyalitas nasabah dikonstruksi dengan menggunakan matriks stokastik. Sementara, prediksi atas kemungkinan berkurangnya frekuensi nasabah yang merupakan agregat dari frekuensi nasabah yang mengundurkan diri dan frekuensi nasabah yang meninggal dunia, dikonstruksi dengan menggunakan model INAR(1) Poisson. Hasil yang diperoleh adalah perusahaan asuransi perlu memberikan perlakuan khusus terhadap nasabah-nasabah yang telah mencapai jangka waktu tertentu dalam pembayaran premi. Hal ini bertujuan untuk menjaga loyalitas nasabah agar risiko yang diakibatkan karena berkurangnya frekuensi nasabah dapat diminimalisir.Kata kunci: prediksi risiko, asuransi, matriks stokastik, model INAR(1) Poisson
Co-Authors Abdulhamid Alzaid Dwi Haryanto Salah Djemili