Safitri, Bella (2026) Pemodelan Dan Verifikasi Formal Pergerakan Nilai Return Investasi Perak Menggunakan Rantai Markov Waktu Diskrit Dan Probabilistic Computation Tree Logic. Other thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Pasar komoditas logam mulia, salah satunya perak, semakin diminati sebagai instrumen investasi alternatif karena potensi imbal hasil yang kompetitif dan perannya sebagai aset lindung nilai. Namun, fluktuasi harga perak yang dipengaruhi oleh faktor ekonomi global, permintaan industri, dan sentimen pasar menciptakan ketidakpastian yang tinggi dalam pengambilan keputusan investasi. Penelitian ini mengembangkan model rantai Markov waktu diskrit (RMWD) yang diverifikasi secara formal menggunakan probabilistic model checking berbasis probabilistic computation tree logic (PCTL) untuk menganalisis perilaku stokastik pergerakan nilai return investasi perak. Data yang digunakan berupa harga penutupan perak harian periode 2020–2025 yang diperoleh dari investing.com, mencakup 1.218 data pengamatan. Model dibentuk melalui proses diskritisasi nilai return ke dalam tiga variasi ruang keadaan (5, 10, dan 15 keadaan) serta pembentukan matriks probabilitas transisi, kemudian diverifikasi menggunakan perangkat lunak PRISM melalui tiga properti temporal PCTL dengan operator next (X), eventually (F), dan globally/always (G). Hasil verifikasi menunjukkan adanya pergeseran dinamika transisi yang signifikan antartahun, di mana periode 2021 menjadi periode dengan peluang transisi menuju nilai return terendah yang paling tinggi, pada periode 2022–2023 memperlihatkan pemulihan bertahap, tahun 2024 menjadi periode dengan probabilitas penghindaran kondisi nilai return terendah yang paling kecil akibat volatilitas tinggi, dan tahun 2025 menampilkan sinyal peningkatan peluang menuju nilai return tertinggi. Pendekatan ini terbukti mampu merepresentasikan dinamika stokastik nilai return perak secara kuantitatif dan diharapkan dapat memberikan wawasan probabilistik yang informatif bagi investor untuk memahami risiko dan peluang investasi perak secara lebih matematis dan terukur.
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The precious metals commodity market, particularly silver, has become increasingly attractive as an alternative investment instrument due to its competitive return potential and its role as a hedging asset. However, fluctuations in silver prices influenced by global economic factors, industrial demand, and market sentiment create high uncertainty in investment decision-making. This research develops a discrete-time Markov chain (DTMC) model that is formally verified using probabilistic model checking based on probabilistic computation tree logic (PCTL) to analyze the stochastic behavior of silver investment return movements. The data used consist of daily silver closing prices for the period 2020-2025 obtained from investing.com, comprising 1,218 observations. The model is constructed through a discretization process of return into three state space variations (5, 10, and 15 states) and the formation of transition probability matrices, which are then verified using the PRISM model checker through three PCTL temporal properties with the next (X), eventually (F), and globally/always (G) operators. The verification results reveal significant shifts in transition dynamics across years, where 2021 exhibited the highest transition probability toward low return conditions, the 2022-2023 period showed a gradual recovery, 2024 recorded the lowest probability of avoiding the lowest return condition due to high volatility, and 2025 showed an increasing signal in the probability toward the highest return condition. This approach has proven capable of quantitatively representing the stochastic dynamics of silver return and is expected to provide informative probabilistic insights for investors to better understand the risks and opportunities of silver investment in a more mathematical and measurable manner.
| Item Type: | Thesis (Other) |
|---|---|
| Uncontrolled Keywords: | Return Perak, Rantai Markov Waktu Diskrit, Probabilistic Computation Tree Logic, Pemodelan dan Verifikasi Formal, PRISM, Silver Return, Discrete-Time Markov Chain, Probabilistic Computation Tree Logic, Formal Modeling and Verification, PRISM |
| Subjects: | Q Science > QA Mathematics > QA274.7 Markov processes--Mathematical models. |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis |
| Depositing User: | Bella Safitri |
| Date Deposited: | 28 Jul 2026 04:13 |
| Last Modified: | 28 Jul 2026 04:13 |
| URI: | http://repository.its.ac.id/id/eprint/138519 |
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