Markovian lifting is an elegant mathematical compromise that trades path-dependent complexity for computational speed without sacrificing the essence of market roughness. This video effectively bridges the gap between high-level stochastic theory and the pragmatic demands of real-time financial engineering.
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Every single time I want to take a step in this process, I don't need the entire path. All I need is the current state.
It makes it very efficient. And we also have other mathematical tools available to us to accomplish different tasks.
finding conditional expectations, solving for options prices, the list goes
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