Optimasi Portofolio Merton dengan Multi-Aset Berisiko Berbasis Fungsi Utilitas HARA Menggunakan Metode Monte Carlo

Zahara, Chasna (2025) Optimasi Portofolio Merton dengan Multi-Aset Berisiko Berbasis Fungsi Utilitas HARA Menggunakan Metode Monte Carlo. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Jumlah investor pasar modal di Indonesia mengalami peningkatan yang signifikan selama beberapa tahun terakhir. Seiring dengan peningkatan angka ini, muncul tantangan dalam pemilihan portofolio untuk konsumsi dan investasi. Penelitian ini mengangkat masalah optimasi portofolio Merton berdasarkan fungsi utilitas Hyperbolic Absolute Risk Aversion (HARA) dalam interval waktu yang terbatas. Portofolio tersebut dibangun oleh dua aset berisiko dan satu aset bebas risiko sehingga investasi tidak terbatas pada satu aset berisiko demi mendapatkan strategi investasi dan konsumsi optimal. Model matematika dari masalah portofolio Merton ditelaah menggunakan persamaan Hamilton-Jacobi-Bellman (HJB). Solusi persamaan HJB dikaji menggunakan metode Monte Carlo sebagai pendekatan numerik sehingga didapatkan hasil bahwa proporsi investasi optimal pada multi-aset berisiko menurun seiring bertambahnya kekayaan. Hal tersebut dipengaruhi oleh preferensi risiko investor terhadap jumlah kekayaannya. Hasil simulasi numerik juga menunjukkan bahwa konsumsi optimal mengalami peningkatan seiring waktu demi mendapatkan utilitas maksimal.
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The number of capital market investors in Indonesia has increased significantly over the past few years. Along with this increase, challenges have arisen in selecting portfolios for consumption and investment. This study addresses the issue of Merton portfolio optimization based on the Hyperbolic Absolute Risk Aversion (HARA) utility function within a finite time interval. The portfolio is constructed using two risky assets and one risk-free asset, ensuring that investments are not limited to a single risky asset in order to achieve optimal investment and consumption strategies. The mathematical model of the Merton portfolio problem is analyzed using the Hamilton-Jacobi-Bellman (HJB) equation. The solution to the HJB equation is examined using the Monte Carlo method as a numerical approach, which shows that the optimal investment proportion in multi-risk assets decreases as wealth increases. This is influenced by the investor's risk preference relative to their wealth. Numerical simulation results also show that optimal consumption increases over time in order to obtain maximum utility.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Optimasi Portofolio, Fungsi Utilitas HARA, Monte Carlo, Multi-Aset Berisiko. Portfolio Optimization, HARA Utility Function, Monte Carlo, Multiple Risky Assets.
Subjects:	Q Science > QA Mathematics > QA274.2 Stochastic analysis Q Science > QA Mathematics > QA401 Mathematical models.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44101-(S2) Master Thesis
Depositing User:	Chasna Zahara
Date Deposited:	01 Aug 2025 02:30
Last Modified:	01 Aug 2025 02:30
URI:	http://repository.its.ac.id/id/eprint/125089

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