Stochastic Processes and their Applications
Выпуски:
Опубликовано на портале: 06-10-2004
J. Michael Harrison, Stanley R. Pliska
Stochastic Processes and their Applications.
1981.
Vol. 11.
No. 3.
P. 215-260.
This paper develops a general stochastic model of a frictionless security market
with continuous trading. The vector price process is given by a semimartingale of
a certain class, and the general stochastic integral is used to represent capital
gains. Within the framework of this model, we discuss the modern theory of contingent
claim valuation, including the celebrated option pricing formula of Black and Scholes.
It is shown that the security market is complete if and only if its vector price
process has a certain martingale representation property. A multidimensional generalization
of the Black-Scholes model is examined in some detail, and some other examples are
discussed briefly.


