Optimasi Portofolio Berbasis Model Markowitz Menggunakan Metode Variational Quantum Eigensolver

Tabassam, Putra Naufal (2026) Optimasi Portofolio Berbasis Model Markowitz Menggunakan Metode Variational Quantum Eigensolver. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Model varians-rerata yang digagas oleh Markowitz merupakan model matematika untuk strategi optimasi portofolio investasi dengan metode pencarian alokasi asset yang memaksimalkan ekspektasi imbal hasil sekaligus meminimalkan varians sebagai risiko. Model tersebut membutuhkan algoritma optimasi yang mumpuni untuk menghasilkan portofolio optimal dari data historis harga pasar. Namun, model optimasi konvensional seringkali mengalami kendala dalam menangkap dinamika pasar modal yang kompleks, terutama saat menangani korelasi antar aset dalam jumlah besar. Untuk mengatasi hal tersebut, tugas akhir ini bertujuan untuk mengoptimalkan alokasi portofolio investasi berdasarkan model varians-rerata yang ditingkatkan lewat kerangka kerja optimasi portofolio hibrida dengan mengintegrasikan prinsip teori permainan potensial eksak ke dalam algoritma Variational Quantum Eigensolver (VQE). Kombinasi ini dilakukan dengan pemetaan permasalahan alokasi portofolio ke dalam bentuk Hamiltonian Ising lewat penyetaraan yang diturunkan dari transformasi QUBO. Untuk mempercepat konvergensi proses optimasi pada komputer kuantum, algoritma pencarian ekuilibrium Nash digunakan sebagai inisialisasi keadaan awal alih-alih menggunakan inisialisasi acak. Hasil simulasi menggunakan data saham indeks IHSG periode 2021–2023 menunjukkan bahwa strategi hibrida GT-VQE secara keseluruhan mengungguli metode klasik dan kuantum murni dengan capaian rasio Sharpe sebesar 1,0132 pada sistem empat aset. Integrasi teori permainan terbukti meningkatkan kestabilan pertumbuhan modal di tengah volatilitas pasar serta mengefisiensikan kedalaman sirkuit kuantum. Temuan ini mengukuhkan potensi pendekatan kuantum-klasik hibrida sebagai solusi praktis yang tangguh untuk optimasi portofolio pada era NISQ.
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The Mean-Variance model introduced by Markowitz is a mathematical framework for investment portfolio optimization strategies that seeks an asset allocation to maximizing expected return while minimizing variance as a measure of risk. This model requires a robust optimization algorithm to generate an optimal portfolio from historical market price data. However, conventional optimization models often face challenges in capturing complex capital market dynamics, particularly when handling correlations among a large number of assets. To address this, this undergraduate thesis aims to optimize investment portfolio allocation based on the Mean-Variance model, enhanced by a hybrid portfolio optimization framework that integrates game theory principles (Exact Potential Game) into the Variational Quantum Eigensolver (VQE) algorithm. This combination is achieved by mapping the portfolio allocation problem into an Ising Hamiltonian form through an equivalence derived from the Quadratic Unconstrained Binary Optimization (QUBO) transformation. To accelerate the convergence of the optimization process on a quantum computer, a Nash Equilibrium search algorithm is utilized as an initial state initialization (warm-start) instead of relying on random initialization. Simulation results using IHSG index stock data for the 2021--2023 period demonstrate that the GT-VQE hybrid strategy overall outperforms both classical and pure quantum methods, achieving a Sharpe Ratio of 1.0132 in a four-asset system. The integration of game theory is proven to enhance capital growth stability amidst market volatility and improve quantum circuit depth efficiency. These discoveries confirm the potential of the hybrid quantum-classical approach as a robust practical solution for portfolio optimization in the Noisy Intermediate-Scale Quantum (NISQ) era.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Econophysics, Game Theory, Ising Hamiltonian, Portfolio Optimization, VQE, Ekonofisika, Game Theory, Hamiltonian Ising, Optimasi Portofolio, VQE
Subjects:	H Social Sciences > HB Economic Theory > Economic forecasting--Mathematical models. H Social Sciences > HC Economic History and Conditions > HC441 Macroeconomics. H Social Sciences > HG Finance H Social Sciences > HG Finance > HG4529.5 Portfolio management H Social Sciences > HG Finance > HG4915 Stocks--Prices Q Science > QA Mathematics > QA184 Algebra, Linear Q Science > QA Mathematics > QA269 Game theory Q Science > QC Physics > QC665.E38 Electric fields. Q Science > QC Physics > QC766.F3 Ferrites
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Physics > 45201-(S1) Undergraduate Thesis
Depositing User:	Putra Naufal Tabassam
Date Deposited:	23 Jul 2026 01:26
Last Modified:	23 Jul 2026 01:26
URI:	http://repository.its.ac.id/id/eprint/136136

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