Pemodelan Dan Verifikasi Formal Nilai Return Investasi Emas Menggunakan Discrete-Time Markov Chain Dan Probabilistic Computation Tree Logic

Khamim, Mohammad Febryan (2026) Pemodelan Dan Verifikasi Formal Nilai Return Investasi Emas Menggunakan Discrete-Time Markov Chain Dan Probabilistic Computation Tree Logic. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Emas menjadi salah satu instrumen investasi yang kian diminati karena mampu menjaga nilai aset dan memberikan potensi keuntungan yang stabil. Sejumlah penelitian telah mengkaji pergerakan harga emas menggunakan berbagai metode, tetapi belum terdapat riset yang secara formal melakukan verifikasi spesifikasi tertentu terhadap hasil pemodelan. Penelitian Tugas Akhir ini mengembangkan model discrete-time Markov chain (DTMC) yang diverifikasi menggunakan probabilistic computation tree logic (PCTL) untuk menganalisis perilaku nilai return investasi emas berdasarkan data harga emas harian dalam satuan rupiah per gram pada 2015 - 2025. Hasil verifikasi menunjukkan bahwa model DTMC yang dibangun mampu merepresentasikan perubahan nilai return harga emas harian berdasarkan matriks probabilitas transisi yang diperoleh dari proses pembagian interval data nilai return. Selain itu, spesifikasi yang dinyatakan dalam PCTL dapat memberikan nilai probabilitas eksak untuk setiap properti yang diverifikasi. Nilai probabilitas hasil verifikasi formal tersebut mampu mengidentifikasi fluktuasi nilai return investasi emas periode 2015 - 2021 dan menunjukkan terjadinya peningkatan performa investasi emas pada beberapa tahun terakhir, yakni 2022 - 2025. Bagi investor, hasil penelitian Tugas Akhir ini dapat memberikan gambaran mengenai kecenderungan pergerakan nilai return investasi emas sekaligus karakteristik risikonya sehingga dapat dimanfaatkan sebagai dasar dalam pengambilan keputusan investasi.
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Gold has become one of the most attractive investment instruments due to its ability to preserve asset value and provide stable profit potential. Numerous studies have examined gold price movements using various approaches; however, there has been limited research that formally verifies specific properties of the resulting models. This undergraduate thesis develops a discrete-time Markov chain (DTMC) model and verifies it using probabilistic computation tree logic (PCTL) to analyze the behavior of gold investment returns based on daily gold price data expressed in Indonesian rupiah per gram from 2015 to 2025. The verification results indicate that the constructed DTMC model is capable of representing daily changes in gold returns through a transition probability matrix obtained from the partitioning of return intervals. Furthermore, the specifications expressed in PCTL provide exact probability values for each verified property. The probabilities obtained from the formal verification process are able to capture fluctuations in gold investment returns during the 2015–2021 period and demonstrate an improvement in gold investment performance in recent years, namely from 2022 to 2025. For investors, the findings of this thesis provide insights into the tendencies of gold investment return movements as well as their risk characteristics, thereby serving as a basis for investment decision-making.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Return Emas, Discrete-Time Markov Chain, Probabilistic Computation Tree Logic Gold Return, Discrete Time Markov Chain, Probabilistic Computation Tree Logic
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:	Mohammad Febryan Khamim
Date Deposited:	22 Jul 2026 01:21
Last Modified:	22 Jul 2026 01:21
URI:	http://repository.its.ac.id/id/eprint/136494

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