Generalized heat diffusion equations with variable coefficients and their fractalization from the Black-Scholes equation

El-Nabulsi R. A., Khalili Golmankhaneh A.

Communications in Theoretical Physics, cilt.73, sa.5, 2021 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 73 Sayı: 5
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1088/1572-9494/abeb05
  • Dergi Adı: Communications in Theoretical Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, INSPEC, zbMATH
  • Anahtar Kelimeler: Black-Scholes equation, generalized Burger's equation, fractal calculus, heat kernels, modified diffusion equations
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this study, we prove that modified diffusion equations, including the generalized Burgers' equation with variable coefficients, can be derived from the Black-Scholes equation with a time-dependent parameter based on the propagator method known in quantum and statistical physics. The extension for the case of a local fractal derivative is also addressed and analyzed.