Constructing C0-Semigroups via Picard Iterations and Generating Functions: An Application to a Black–Scholes Integro-Differential Operator

An alternative approach is proposed for constructing a strongly continuous semigroup based on the classical method of successive approximations, or Picard iterations, together with generating functions. application to Black–Scholes integro-differential operator which arises in pricing European options under jump-diffusion dynamics provided. The expressed as Mellin convolution time-inhomogeneous jump and kernel Other applications heat transport equations are also given. connection Adomian decomposition explored.