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All Journal Jurnal Penyuluhan FORUM STATISTIKA DAN KOMPUTASI Forum Pasca Sarjana CAUCHY: Jurnal Matematika Murni dan Aplikasi Al-Jabar : Jurnal Pendidikan Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jambura Journal of Mathematics Jambura Geoscience Review InPrime: Indonesian Journal Of Pure And Applied Mathematics Jurnal Statistika dan Matematika (Statmat) Jurnal Statistika dan Aplikasinya Makara Human Behavior Studies in Asia Milang Journal of Mathematics and Its Applications Jurnal Matematika Integratif MILANG Journal of Mathematics and Its Applications Limits: Journal of Mathematics and Its Applications
I Gusti Putu Purnaba
Departemen Matematika, Fakultas Matematika Dan Ilmu Pengetahuan Alam, Institut Pertanian Bogor
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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Pengaruh Inflasi terhadap Strategi Optimal Investasi dan Konsumsi dengan Model Stokastik Dara Irsalina; Retno Budiarti; I Gusti Putu Purnaba
Limits: Journal of Mathematics and Its Applications Vol. 19 No. 1 (2022): Limits: Journal of Mathematics and Its Applications Volume 19 Nomor 1 Edisi Me
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Abstract

The aim of this study is to investigate an optimal investment-consumption strategy under inflation rate with interest rate is described by Cox-Ingersol-Ross (CIR) model and volatility of the stock price is defined by Heston’s volatility model. A dynamic programming principle is used to obtain a Hamilton Jacobi Bellman (HJB) equation for the value function and choose a power utility function as utility function. The explicit solution of optimal investment and consumption are acquired with using separate variable and approach variable technique. The parameter’s values are approached by Euler-Maruyama method and Ordinary Least Square (OLS) method. Assumed that the portfolio of the investor contains a risk-free asset and a risk asset. Monthly historical data of TLK stock is used as risk asset and monthly historical data of BI 7-Day (Reverse) Repo Rate (BI7DRR) is used as risk-free asset, we obtain that the proportion of investment in stock is directly proportional to return of stock and the inflation rate does not have an impact on proportion investment in the stock. Meanwhile the optimal consumption of wealth is directly proportional to investor’s wealth and inversely proportional with inflation rate, which is the investor should consume less money of his wealth when the inflation rate increases.
Mathematical Model of Joint Life Term Insurance Premiums under Inflation, Interest Rate, and Dependent Mortality Habel, Ine Febrianti; Purnaba, I Gusti Putu; Budiarti, Retno
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 2 (2026): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i2.35690

Abstract

Multilife insurance refers to a contract that covers two or more lives simultaneously, with joint life insurance representing a key form in which the benefit is paid upon the first death among the insured individuals. The lifetimes of insured individuals are typically not independent, as they may be influenced by shared environmental, health, or behavioral factors, leading to mortality dependence. Inflation and interest rates also play critical roles in determining the present value of benefits and premiums. However, most previous studies have examined either mortality dependence or macroeconomic effects in isolation. This study aims to develop a comprehensive mathematical model for determining joint life term insurance premiums that simultaneously incorporates mortality dependence through the Gumbel copula and interest rate and inflation through the Fisher equation. The model integrates demographic and economic risk components within a unified actuarial valuation framework, providing a more realistic representation of premium dynamics under varying financial conditions. Simulation results indicate that premiums incorporating inflation are consistently higher than those without inflation, whereas higher nominal interest rates result in lower premium levels. These findings reflect the theoretical relationship between inflation, real interest rates, and the time value of money. The study further introduces an elasticity-based analysis that quantifies the sensitivity of premiums to changes in inflation and interest rates, demonstrating nonlinear yet economically meaningful responses across different age structures of insured spouses. The results highlight the importance of jointly modeling mortality dependence and economic variables to enhance pricing accuracy and fairness in life insurance. The proposed model offers practical relevance for actuaries in premium determination, assists insurers in risk management and product design, and supports the development of resilient pricing strategies under inflationary and interest.
Co-Authors A. D. GARNADI Adilla, Indrya Amiruddin Saleh Amri Jahi Amri Jahi Amri Jahi Auliya Fithry Aunuddin . Awatif Berlian Setiawaty D. C. LESMANA D. S. Rahmawati Daniel Happy Putra Dara Irsalina Darwis S Gani Darwis S. Gani Darwis S. Gani Darwis S. Gani Dian Puspita Dian Puspita Djoko Susanto Djoko Susanto Donny Citra Lesmana Dwi Fidiana E. H. NUGRAHANI Erliana, Windiani Fendy Septyanto Fikri, Miftahul Fikriyah, Laila Qudrah Furlo Gilbert Godfrey Habel, Ine Febrianti Hadi Sumarno I Gede Setiawan Adi Putra I W. MANGKU I W. MANGKU I Wayan Mangku I. MAULIDI I. WIDIYASTUTI Indahwati Indrya Adilla Intansari, Kumala Iwan Tjitradjaja Iwan Tjitradjaja Iwan Tjitradjaja J. S. SELEKY Kelvin Gunawan Khairiati, Alfi Laila Qudrah Fikriyah Luky Adrianto M. FIKRI Ma'mun Sarma Maharani, Ardella Manjaruni, Vivin Aprilia Mokhamad O Royani Muh Hatta Jamil Muhammad Yusuf Sulaiman Nabila, Amanda Nahrul Hayati Najib, Mohammad Khoirun Nur Agustiani Pang S. Asngari Pang S. Asngari Prihandoko . Prihandoko Prihandoko Prihandoko S Prihandoko S Purwoko, Agus R. BUDIARTI Rafika Septiany Rahmah, Salsabilla Rahmawati, D. S. Retno Budiarti Rizki, Kurniadi Ruhiyat Ruhiyat Ruhiyat Ruhiyat Ruhiyat, Ruhiyat S. ARTIKA S. NURDIATI S. UTAMI Sapar . Sapar Sapar Septiany, Rafika Setyawan, Binar Aulia Sri Nurdiati Sugiyanta Sugiyanta Sulaiman, Muhammad Yusuf Syifa Aulia Tri Andika Julia Putra Vivin Manjaruni W. ERLIANA Windiani Erliana Windiani Erliana Windiani Erliana Y. ARBI Yolwi Dyatma Yolwi Dyatma Yuda Ardiansyah Yuda Ardiansyah Yudasril Yudasril _ Aunuddin