Lie Symmetry Group Methods

This chapter introduces Lie Symmetry Group Methods as a powerful tool which can be used to algorithmitically solve partial differential equations. The latter feature prominently in mathematical finance, and we introduce Lie Symmetry methods by using them to algorithmitically solve the most famous partial differential equation in mathematical finance, namely the Black-Scholes partial differential equation. Subsequently we recall with proofs important results from the literature, and we demonstrate in subsequent chapters that these results cover precisely those partial differential equations which arise naturally under the benchmark approach. The chapter presents proofs in a considerable amount of detail with the aim of highlighting the algorithmic nature of Lie Symmetry Methods but also to encourage readers to apply these methods to their fields of interest.

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