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Constructing c0-semigroups via picard iterations and generating functions: An application to a black���scholes integro-differential operator

Journal Article


Abstract


  • 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. An application to a Black���Scholes integro-differential operator which arises in the pricing of European options under jump-diffusion dynamics is provided. The semigroup is expressed as the Mellin convolution of time-inhomogeneous jump and Black���Scholes kernel functions. Other applications to the heat and transport equations are also given. The connection of the proposed approach to the Adomian decomposition method is explored.

Publication Date


  • 2021

Citation


  • Rodrigo, M. R. (2021). Constructing c0-semigroups via picard iterations and generating functions: An application to a black���scholes integro-differential operator. Mathematics, 9(6), 1-15. doi:10.3390/math9060589

Scopus Eid


  • 2-s2.0-85102952639

Web Of Science Accession Number


Start Page


  • 1

End Page


  • 15

Volume


  • 9

Issue


  • 6

Place Of Publication


Abstract


  • 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. An application to a Black���Scholes integro-differential operator which arises in the pricing of European options under jump-diffusion dynamics is provided. The semigroup is expressed as the Mellin convolution of time-inhomogeneous jump and Black���Scholes kernel functions. Other applications to the heat and transport equations are also given. The connection of the proposed approach to the Adomian decomposition method is explored.

Publication Date


  • 2021

Citation


  • Rodrigo, M. R. (2021). Constructing c0-semigroups via picard iterations and generating functions: An application to a black���scholes integro-differential operator. Mathematics, 9(6), 1-15. doi:10.3390/math9060589

Scopus Eid


  • 2-s2.0-85102952639

Web Of Science Accession Number


Start Page


  • 1

End Page


  • 15

Volume


  • 9

Issue


  • 6

Place Of Publication