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Hard · Stochastic Calculus · Quant Trader interview question · Feynman-Kac, PDE, Stochastic Calculus, Conditional Expectation
Consider the partial differential equation (PDE): $ \frac{\partial u}{\partial t} + \frac{1}{2} \sigma^2 \frac{\partial^2 u}{\partial x^2} = 0 $ with terminal condition $u(T, x) = g(x)$, where $ \sigma $ is a constant volatility. According to the Feynman-Kac formula, what is the probabilistic representation of the solution $u(t, x)$?