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I came across a generalized Black-Scholes equation formulation in this paper. Let me highlight the basic idea below. Consider a random field $W(t,T)$ where for a fixed $T$, $W$ is a Brownian motion ...

Consider the Black-Scholes model $$ dS(t) = \mu(t) S(t) dt + \sigma(t) S(t) dW^{\mathbb{P}}(t) $$ $$ dB(t) = r(t) B(t) dt$$ Steele shows now in "Stochastic Calculus & Financial Applications" (Ch. ...