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All Journal Journal of the Indonesian Mathematical Society BAREKENG: Jurnal Ilmu Matematika dan Terapan
Dwi Ertiningsih
Jurusan Matematika, FMIPA, Universitas Gadjah Mada
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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PERFORMANCE LOSS QUANTIFICATION IN KERNEL DENSITY ESTIMATION FOR ACTUARIAL AND FINANCIAL ANALYSIS Untsa, Shafira Fauzia; Susyanto, Nanang; Qoiyyimi, Danang Teguh; Ertiningsih, Dwi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp2029-2038

Abstract

Accurately estimating aggregate loss distributions is critical in actuarial and financial risk assessment, as it underpins effective risk analysis and the development of mitigation strategies. However, incorrect parametric assumptions can lead to biased risk estimates and underestimated losses. Non-parametric methods, such as Kernel Density Estimation (KDE), offer a flexible alternative by generating smooth empirical probability density functions (PDFs) directly from sample data without assuming a specific distributional form. This study examines the impact of dependence structures on risk measures by applying KDE with a Gaussian kernel to estimate aggregate loss distributions. To quantify the effects of ignoring dependence, we introduce the concept of performance loss, focusing on variance, Value at Risk (VaR), and Tail Value at Risk (TVaR). The results show that performance loss increases with the correlation coefficient, indicating that higher dependency leads to greater underestimation of risk. Additionally, higher confidence levels amplify performance loss for VaR and TVaR, underscoring the sensitivity of these measures to tail behavior. These findings highlight the importance of incorporating dependence structures in risk modeling to avoid misleading evaluations. The implications are particularly relevant for disaster risk management in Central Asia, where overlooking interdependencies in seismic losses could result in inadequate financial and actuarial strategies.
Analysis of Earthquake Potential along the Coastal Region of South Java using Semi-Markov Models as a Tsunami Mitigation Puteri, Athaya Rahma; Sa'diyah, Halimatus; Fauziah, Alfia Nur; Simbolon, Christina Agustin Raphonhita; Firmansyah, Ramadhani Latief; Ertiningsih, Dwi
Journal of the Indonesian Mathematical Society Vol. 32 No. 1 (2026): MARCH
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v32i1.1556

Abstract

This study applies a semi-Markov model to assess earthquake occurrence in the South Java coastal region. The main objective is to forecast earthquakes in this area, considering three key factors: geographic location, timing, and seismic magnitude. The South Java coastal region is chosen for this study due to its proximity to the island of Java, the economic hub of Indonesia. The study divides the South Java coastal region into five distinct zones and categorizes earthquakes into three magnitude groups. The results predict that earthquakes will occur in the South Coast regions of East Java, Central Java, or West Java between December 26, 2022, and November 20, 2023. Additionally, projections suggest that earthquakes are likely to occur in East Java, West Java, or Banten between November 21, 2023, and December 31, 2030. The estimated magnitudes range from 5 to 6 Mw. The findings also indicate that no tsunamis are expected along the South Java coast until 2030. Model validation using the Mean Absolute Percentage Error (MAPE) results in a value of 4.224\%. This confirms the high accuracy of the predictions. Although no tsunamis are forecasted, the public must remain alert and prepared for the anticipated earthquakes. These findings provide important insights for disaster mitigation and emphasize the need for ongoing monitoring, early warning systems, and community preparedness to minimize potential risks
Co-Authors Fauziah, Alfia Nur Firmansyah, Ramadhani Latief Puteri, Athaya Rahma Qoiyyimi, Danang Teguh Sa'diyah, Halimatus Simbolon, Christina Agustin Raphonhita Susyanto, Nanang Untsa, Shafira Fauzia