A NEW MARKET MODEL IN THE LARGE VOLATILITY CASE

Yukio Hirashita (Japan)

Received March 11, 2008

References:

[1] F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Political Economy 81 (1973), 637-654. [2] M. M. Christensen, On the history of the growth optimal portfolio, University of Southern Denmark, Working Paper, 2005. [3] Y. Hirashita, Game pricing and double sequence of random variables, Preprint 2007, arXiv:math.OC/0703076. [4] Y. Hirashita, Delta hedging without the Black-Scholes formula, Far East J. Appl. Math. 28 (2007), 157-165. [5] J. Hull, Options, Futures and other Derivatives, Prentice Hall, New Jersey, 2003. [6] D. G. Luenberger, Investment Science, Oxford University Press, Oxford, 1998. [7] B. Æksendal, Stochastic Differential Equations, Springer, Berlin, 1998. [8] P. A. Samuelson, The “Fallacy” of maximizing the geometric mean in long sequences of investing or gambling, Proc. Nat. Acad. Sci. USA 68 (1971), 2493-2496. [9] A. N. Shiryaev, Essentials of Stochastic Finance, World Scientific, Singapore, 1999.

Keywords and phrases: complete market, rational price, geometric price, martingale price.