A Terminal Condition in Linear Bond-pricing Under Symmetry Invariance
Rivoningo Maphanga, Sameerah Jamal
Abstract
Abstract In this paper, we examine a general bond-pricing model with respect to its solutions that satisfy a given terminal condition. Firstly, we obtain reversible transformations that change the model to a classical and well known partial differential equation, the one dimensional heat equation. We further show that the terminal condition is transformed into a nonsmooth initial condition. The important result that emerges is that the Lie symmetries are adopted to solve the equation subject to its unique configuration of initial conditions.
Topics & Concepts
Terminal (telecommunication)MathematicsHomogeneous spaceSymmetry (geometry)Partial differential equationHeat equationDifferential equationApplied mathematicsDifferential (mechanical device)Mathematical analysisGeometryComputer sciencePhysicsTelecommunicationsThermodynamicsMathematical and Theoretical Epidemiology and Ecology ModelsNonlinear Differential Equations AnalysisNonlinear Partial Differential Equations