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Modelling The Probability of Insurance Company’s Bankruptcy Using Integro-Differential Equation and Its Simulation Maulida, Ghafira Nur; Prabowo, Agung; Supriyanto, Supriyanto; Mamat, Mustafa; Sukono, Sukono
Indonesian Actuarial Journal Vol. 1 No. 1 (2025): Indonesian Actuarial Journal
Publisher : Persatuan Aktuaris Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.65689/iajvol01no1pp084-094

Abstract

Ruin is one of the risks that insurance companies may face. Therefore, modeling the probability of ruin is a crucial aspect of risk management. This study aims to model and analyze the probability of ruin in insurance companies using integro-differential equations, assuming that the claim size follows a mixtures of two exponential distributions. The research methods are literature study and numerical simulation with phyton. Numerical calculations were performed using Python programming, and the results are presented in tables and graphs to facilitate analysis. The model is applied to three different cases. The findings indicate that the probability of ruin is inversely proportional to the initial capital and premium loading, while it is directly proportional to the expected value of claims. In other words, the probability of ruin decreases significantly as the initial capital and premium loading increase, whereas it increases as the expected value of claims rises. Therefore, the greater the surplus of an insurance company, the lower the probability of ruin.
Kajian Perbandingan Turunan dan Integral Fraksional Riemann–Liouville, Caputo, dan Konformabel serta Aplikasinya Gunawan, Gani; Rusyaman, Endang; Sukono, Sukono; Carnia, Ema
Jurnal Matematika Integratif Vol 21, No 2: Oktober 2025
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v21.n2.68569.245-258

Abstract

Penelitian ini membandingkan tiga definisi utama turunan fraksional, yaitu Riemann–Liouville, Caputo, dan Konformabel, dalam pemodelan sistem dinamis yang melibatkan efek memori. Populasi kajian adalah operator turunan fraksional sebagai generalisasi kalkulus klasik berorde bukan bilangan bulat. Intervensi dilakukan melalui pendekatan analitik dan numerik, meliputi kajian sifat dasar operator, analisis eksistensi solusi, dan penerapannya pada persamaan diferensial fraksional linear sederhana. Perbandingan difokuskan pada kesesuaian terhadap sifat kalkulus klasik, bentuk solusi, dan karakter peluruhan sistem. Hasil menunjukkan bahwa turunan Riemann–Liouville dan Caputo menghasilkan solusi berbasis fungsi Mittag–Leffler dengan peluruhan lambat, sehingga sesuai untuk fenomena dengan memori jangka panjang, sedangkan turunan Konformabel menghasilkan solusi eksponensial dengan peluruhan lebih cepat dan efisiensi komputasi yang lebih tinggi. Rentang waktu kajian difokuskan pada orde fraksional α = 1/2 sebagai representasi perilaku umum ketiga definisi. Temuan ini menegaskan bahwa pemilihan operator fraksional harus disesuaikan dengan tujuan analisis dan konteks aplikasi, khususnya antara kebutuhan representasi efek memori dan efisiensi analitik
Co-Authors Abdul Talib Bon Abiodun Ezekiel Owoyemi Achmad Bachrudin Adhitya Ronnie Effendie, Adhitya Ronnie Agung Prabowo Agung Prabowo Agung Prabowo Agus Santoso Agus Santoso Agus Sugandha Agustini Tripena Br Surbakti Aisyah Nurul Aini Amalia, Hana Safrina Amitarwati, Diah Paramita Apipah Jahira, Juwita Asep K Supriatna Asep Saepulrohman Asep Solih Awalluddin, Asep Solih Asri Rula Hanifah Audina, Maudy Afifah Aulia Kirana Aziza Ayu Nurjannah Bakti Siregar Banowati, Puspa Dwi Ayu Basuki , Basuki Basuki Bayyinah, Ayyinah Nur Betty Subartini Bimasota Aji Pamungkas bin Mamat, Mustafa Budi Pratikno Candra Budi Wijaya Carissa, Katherine Liora Dara Selvi Mariani Dedy Rosadi Dedy Rosadi Dewi Ratnasari DEWI RATNASARI Dhika Surya Pangestu Diah Chaerani Diah Paramita Amitarwati Diana Ekanurnia Dianti, Estu Putri Dihna, Elza Rahma Dini Aulia Dwi Susanti Dwi Susanti Dwi Susanti Dwi Susanti Dwi Susanti Dwi Susanti Eddy Djauhari Edi Kurniadi Ema Carnia Emah Suryamah, Emah Eman Lesmana Endang Rusyaman Endang Soeryana Hasbullah Fasa, Rayyan Al Muddatstsir Febrianty, Popy Firdaus, Muhammad Rayhan Forman Ivana S. S. S. Gani Gunawan Ghazali, Puspa Liza Grida Saktian Laksito Hadiana, Asep Id Haq, Fadiah Hasna Nadiatul Hasbullah, Soeryana Hasriati Hasriati Hazelino Rafi Pradaswara Herlina Napitupulu Herlina Napitupulu Hidayana, Rizki Apriva Ibrahim M Sulaiman Ihda Hasbiyati Iin Irianingsih Ira Sumiati Ismail Bin Mohd Januaviani, Trisha Magdalena Adelheid Jumadil Saputra Jumadil Saputra Kahar, Ramadhina Hardiva kalfin Kalfin Kalfin, Kalfin Khairi, M. Ihsan Labitta, Kirana Fara Laksito, Grida Saktian M. Ihsan Khairi Maraya, Nisrina Salsabila Maulana Malik Maulida, Ghafira Nur Ma’mur, Lutfi Praditia Melina Melina Mochamad Suyudi Mohamad Nurdin, Dadang Muhammad Arief Budiman Muhammad Iqbal Al-Banna Ismail Mustafa Mamat Mustafa Mamat Mustafa Mamat Mustafa Mamat Mustafa Mamat Nabilla, Ulya Nahda Nabiilah Nita Rulianah Noriszura Ismail Norizan Mohamed Novianti, Saqila Novieyanti, Lienda Novinta S, Fujika Novitasari, Ela Nugraha, Dwita Safira Nur Mahmudah Nurdyah, Himda Anataya Nurfadhlina Abdul Halim Nurul Fadilah Okta Yohandoko, Setyo Luthfi Pardede, Ester Priyatna, Yayat Puspa Liza Ghazali Putri, Aulya Putri, Linda Damayanti Putri, Sherina Anugerah Raharjanti, Amalia Rahman, Rezki Aulia Ramdhania, Tya Shafa Ratih Kusumadewi Riadi, Nadia Putri Riaman Riaman Riaman Riaman Riaman Riaman Riaman Riaman, Riaman Riaman, Riaman Rini Cahyandari Riza Adrian Ibrahim Rosadi, D. - Rulianah, Nita Saefullah, Rifki Salamiah, Mia Salih, Yasir Sampath, Sivaperumal Saputra, Jumadil Shindi Adha Gusliana Sianturi, Sri Novi Elizabeth Sisilia Sylviani Siti Sabariah Abas Soeryana Hasbullah Sri Purwani Stanley Pandu Dewanto Subanar - Subanar . Subanar Subanar Subiyanto Subiyanto Sudradjat Supian Suhaimi, Nurnisaa binti Abdullah Sulastri, S Sumiati, Ira Supian, Sudradjat Supriyanto Supriyanto Suroto Suroto Susanto, Sunarta Sutiono Mahdi Sutisna, Sarah Suyudi, Mochamad Suyudi, Mochammad T.P Nababan Tampubolon, Carlos Naek Tua Tika Fauzia Tiswaya, Waway Titi Purwandari Titin Herawati Umar A Omesa Valentina Adimurti Kusumaningtyas Verrany, Maria Jatu Vimelia, Willen Wahid, Alim Jaizul Wan Muhamad Amir W Ahmad Widyani, Azizah Rini Wiliya Wiliya Yasir Salih Yasmin, Arla Aglia Yhenis Apriliana Yulianus Brahmantyo Yulison Herry Chrisnanto Yuningsih, Siti Hadiaty Yuyun Hidayat Zahra, Ami Emelia Putri Zinedine Amalia Noor Mauludy Reihan