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The tool of Series solutions in Quantitative Finance

Explain the tool of Series solutions in Quantitative Finance.

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Series solutions: If your equation is linear and they mostly all are in quantitative finance then you might be capable to solve a particular problem with adding together the solutions of many problems. Series solutions are while you decompose the solution in a (potentially infinite) sum of simple functions, as cosines and sines, or a power series. It is the case, for illustration, with barrier options consisting of two barriers, one below the current asset price and another above.

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