Lie Analysis for Partial Differential Equations in Finance
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Weather derivatives are financial tools used to manage the risks related to changes in the weather and are priced considering weather variables such as rainfall, temperature, humidity and wind as the underlying asset. Some recent researches suggest to model the amount of rainfall by considering the mean reverting processes. As an example, the Ornstein Uhlenbeck process was proposed by Allen  to model yearly rainfall and by Unami et al.  to model the irregularity of rainfall intensity as well as duration of dry spells. By using the Feynman-Kac theorem and the rainfall indexes we derive the partial differential equations (PDEs) that governs the price of an European option. We apply the Lie analysis theory to solve the PDEs, we provide the group classification and use it to find the invariant analytical solutions, particularly the ones compatible with the terminal conditions.
Nhangumbe, C.V. 2019. Lie Analysis for Partial Differential Equations in Finance. . ,Faculty of Science ,Department of Maths and Applied Maths.