Analog of the black-scholes formula for option pricing under conditions of (B, S, X)-incomplete market of securities with jumps

• Date: 2000
• Main Authors: Zhuravyts'kyi, D. G., Kalemanova, A. V., Svishchuk, A. V., Журавицкий, Д. Г., Калеманова, А. В., Свищук, А. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2000
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4434
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We describe a (B, S,X )-incomplete market of securities with jumps as a jump random evolution process that is a combination of an ltô process in random Markov medium and a geometric compound Poisson process. For this model, we derive the Black-Scholes equation and formula, which describe the pricing...