medium · Quantitative Finance stochastic
In the context of the Feynman-Kac formula, what is the significance of the 'Initial Value Problem' versus a 'Terminal Value Problem'?
- Monte Carlo methods estimate the expectation numerically forward in time, while PDEs solve it via a spatial grid.
- Expectations can be computed from any starting time by conditioning on the state variable observed at that time.
- Finance usually solves terminal value problems, where the payoff is known at T and we solve backward to t.
- Feynman-Kac also applies directly to initial value problems, such as the heat equation in physics.
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