Model suku bunga jangka pendek berbasis grup Lie matriks heisenberg berdimensi lima
DOI:
https://doi.org/10.33387/dpi.v14i2.10246Kata Kunci:
Grup Lie Heisenberg, Matriks, Persamaan Diferensial Stokastik, Persamaan Dinamik, Suku BungaAbstrak
Teori Lie dapat diterapkan dalam berbagai bidang ilmu seperti matematika keuangan. Menggunakan persamaan diferensial stokastik melalui gerak Brown, suatu ruang keadaan dinamik dapat ditentukan. Penelitian ini bertujuan untuk mengkonstruksi model suku bunga menggunakan grup matriks Heisenberg berdimensi lima. Sifat ini memberikan dua pasang interaksi konjugat yang terikat pada satu pusat berdasarkan pada bracket Lie-nya. Di model terdahulu, interaksinya sangat linear dan terbatas. Di model dimensi 5, suku bunga jangka pendek bisa memodelkan interaksi silang (cross-coupling) yang rumit seperti guncangan pasar (market shocks) yang memengaruhi ekspektasi inflasi, yang pada gilirannya menekan suku bunga jangka pendek secara non-linear. Dalam penelitian ini dibuktikan bahwa ruang keadaan dinamik yang diperoleh melalui grup matriks Heisenberg berdimensi lima mempunyai bentuk umum di mana dan adalah proses Wiener independen. Lebih jauh, model suku bunga juga diperoleh dalam bentuk umum di mana adalah konstanta. Untuk penelitian selanjutnya, suku bunga yang dikonstruksi melalui grup matriks Heisenberg berdimensi masih terbuka untuk dikaji.
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