EXPLICIT SOLUTION PROCESSES FOR NONLINEAR JUMP-DIFFUSION EQUATIONS

Uenal G., Turkeri H., Khalique C. M.

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, cilt.17, sa.3, ss.281-310, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 3
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1142/s1402925110000908
  • Dergi Adı: JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.281-310
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

Recent studies have shown that the nonlinear jump-diffusion models give results which are in agreement with financial data. Here we provide linearization criteria together with transformations which linearize the nonlinear jump-diffusion models with compound Poisson processes. Furthermore, we introduce the stochastic integrating factor to solve the linear jump-diffusion equations. Extended Cox-Ingersoll-Ross, Brennan-Schwartz and Epstein models are shown to be linearizable and their explicit solutions are presented.