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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

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

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.

Regular admissible wealth processes are necessarily of Black

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

David Grow Dirk Rohmeder Suman Sanyal

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.
There are 10 citations in total.

Details

Journal Section Articles
Authors

David Grow This is me

Dirk Rohmeder This is me

Suman Sanyal This is me

Publication Date August 1, 2014
Published in Issue Year 2014 Volume: 2 Issue: 2

Cite

APA Grow, D., Rohmeder, D., & Sanyal, S. (2014). Regular admissible wealth processes are necessarily of Black-Scholes type. New Trends in Mathematical Sciences, 2(2), 117-124.
AMA Grow D, Rohmeder D, Sanyal S. Regular admissible wealth processes are necessarily of Black-Scholes type. New Trends in Mathematical Sciences. August 2014;2(2):117-124.
Chicago Grow, David, Dirk Rohmeder, and Suman Sanyal. “Regular Admissible Wealth Processes Are Necessarily of Black-Scholes Type”. New Trends in Mathematical Sciences 2, no. 2 (August 2014): 117-24.
EndNote Grow D, Rohmeder D, Sanyal S (August 1, 2014) Regular admissible wealth processes are necessarily of Black-Scholes type. New Trends in Mathematical Sciences 2 2 117–124.
IEEE D. Grow, D. Rohmeder, and S. Sanyal, “Regular admissible wealth processes are necessarily of Black-Scholes type”, New Trends in Mathematical Sciences, vol. 2, no. 2, pp. 117–124, 2014.
ISNAD Grow, David et al. “Regular Admissible Wealth Processes Are Necessarily of Black-Scholes Type”. New Trends in Mathematical Sciences 2/2 (August 2014), 117-124.
JAMA Grow D, Rohmeder D, Sanyal S. Regular admissible wealth processes are necessarily of Black-Scholes type. New Trends in Mathematical Sciences. 2014;2:117–124.
MLA Grow, David et al. “Regular Admissible Wealth Processes Are Necessarily of Black-Scholes Type”. New Trends in Mathematical Sciences, vol. 2, no. 2, 2014, pp. 117-24.
Vancouver Grow D, Rohmeder D, Sanyal S. Regular admissible wealth processes are necessarily of Black-Scholes type. New Trends in Mathematical Sciences. 2014;2(2):117-24.