  In common finance literature, Black-Scholes partial differential equation of
option pricing is usually derived with no-arbitrage principle. Considering an
asset market, Merton applied the Hamilton-Jacobi-Bellman techniques of his
continuous-time consumption-portfolio problem, deriving general equilibrium
relationships among the securities in the asset market. In special case where
the interest rate is constant, he rederived the Black-Scholes partial
differential equation from the general equilibrium asset market. In this work,
I follow Cox-Ingersoll-Ross formulation to consider an economy which includes
(1) uncertain production processes, and (2) the random technology change.
Assuming a random production stochastic process of constant drift and variance,
and assuming a random technology change to follow a log normal process, the
equilibrium point of this economy will lead to the Black-Scholes partial
differential equation for option pricing.
