Regular admissible wealth processes are necessarily of Black-Scholes type

• Main Authors: David Grow, Dirk Rohmeder, Suman Sanyal
• Format: Article
• Language: English
• Published: BİSKA Bilisim Company 2014-10-01
• Series: New Trends in Mathematical Sciences
• Subjects: Black-Scholes; Option pricing; Geometric Brownian motion
• Online Access: https://ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=32
• ISSN: 2147-5520; 2147-5520

We show that for a complete market where the stock price uncertainty is driven by a Brownian motion, there exists only one admissible wealth process which is a regular deterministic function of the time and the stock price. In particular, if the stock price is modeled by geometric Brownian motion then the Black-Scholes process is the only regular admissible wealth process.