Regular admissible wealth processes are necessarily of Black-Scholes type

Year 2014, Volume: 2 Issue: 2, 117 - 124, 01.08.2014

David Grow Dirk Rohmeder Suman Sanyal

https://izlik.org/JA98JN73NZ

Abstract

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

Keywords

Black-Scholes , Option pricing; Geometric Brownian motion

Regular admissible wealth processes are necessarily of Black

https://izlik.org/JA98JN73NZ

Abstract

References

• Bensoussan, A.; On the theory of option pricing. Acta Applicandae Mathematicae 2(1984), 139-158.
• Black, F. and Scholes, M.; The pricing of options and corporate liabilities. Journal of Political Economy 81 (1973), 637-659.
• Harrison, J.M. and Pliska, S.R.; A stochastic calculus model of continuous trading: complete markets. Stochastic Processes and their Applications 15 (1983), 313-316.
• Feynman, R.P.; Space-time approach to nonrelativistic quantum mechanics. Reviews of Modern Physics 20 (1948), 367-387.
• Friedman, A.; Partial Differential Equations of Parabolic Type. Prentice-Hall, Engle- wood Cliffs, New Jersey (1964).
• Kac, M.; On distributions of certain Wiener functionals. Transactions of the American Mathematical Society 65 (1949), 1-13.
• Karatzas, I.; On the pricing of American options. Applied Mathematics and Optimization 17 (1988), 37-60.
• Karatzas, I. and Shreve, S.E.; Brownian Motion and Stochastic Calculus (second edition). Springer Verlag, New York (1991).
• Merton, R.C.; Theory of rational option pricing. The Bell Journal of Economics and Management Science 4 (1973), 141-183.
• Rohmeder, D.; Pricing of European options. M.S. thesis, Missouri University of Science and Technology, Rolla, Missouri, USA, 2003.