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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 ...

Assume $X_t$ is an Ornstein-Uhlenbeck process in the form of $$ d X_t = -\alpha X_t dt + \sigma dB_t $$ Is there an exponential bound (large-deviation bound) for $$ P\left( \max_{t\le T} |X_t| \ge z \...

Given a "hybrid" Black-Scholes Hull White (BSHW) model. That is, the stock price is modelled by a Black Scholes SDE: \begin{equation} dS(t) = \mu(t)S(t)dt + \sigma_{S}(t)S(t)dW^{\mathbb{P}}_{S}(t) \...