Abstract
Operational risk is one of the common risks in organizations, especially in banks, which has a wide range of errors in individual performance or system failure with process problems. In this paper, the mathematical model of operational risk to calculate the probability of the organization being convinced is presented, which is in the form of a Volterra integro-differenial equations and is solved by the Adomian decomposition method (ADM). Also, the ADM is applied in one dimension as semi-Adomian decomposition method (s-ADM). Comparison of results demonstrates proficiency of the ADM and s-ADMin this model.
Similar content being viewed by others
References
Basel committee on banking supervision, working paper on the regulatory treatment of operational risk. Bank Int. Settlement. 39, 1–39 (2001b)
Basel Committee on Banking Supervision: Bank for International Settlements. https://www.bis.orgURL www.bis.org (2001)
Bahiraie, A., Alipour, M., Sadiq, R.: Option pricing accumulated with operational risk. Adv. Math. Financ. Appl. 5(4), 437–448 (2020)
Ladopoulos, E.G.: Non-linear integro- differential equations for risk management analysis: further developments spaces. Univ. J. Integr. Equ. 4, 13–20 (2016)
Makroglu, A.: Integral equations and actuarial risk management: some models and numerics. Math. Model. Anal. 8(2), 143–154 (2003)
Knessl, C., Peters, C.S.: Exact and asymptotic solutions for the time dependent problem of collective ruin II. Siam. J. Apple. Math. 54, 1745–1767 (1994)
Wazwaz, A.M.: Partial Differential Equations and Solitary Waves Theory. Nonlinear Physical Science. Springer, Berlin, Heidelberg (2009)
Fariborzi Araghi, M.A., Sadigh Behzadi, S.H.: Solving nonlinear Volterra Fredholm integro-differential equations using the modified Adomian decomposition method, computational methods in applied mathematics 9(4), 1–11 (2009)
Agom, E.U., Ogunfiditimi, F.O.: Numerical solution of third order time-invariant linear Differential equation by Adomian decomposition method. Int. J. Eng. Sci. 2319–1805,(2016)
Adomian, G.: Nonlinear Stochastic System Theory and Applications to Physics. Kluwer, Dordrecht (1989)
Vahidi, A.R., Damercheli, T.: A modified ADM for solving systems of linear Fredholm integral equations of the second kind. Appl. Math. Sci 6(26), 1267–1273 (2012)
Bakodah, H.O., Al Qarni, A.A., Banaja, M.A., Zhou, Qin, Moshokoa, Seithuti P.: Anjan Biswas, bright and dark thirring optical solitons with improved Adomian decomposition method. Optik 130, 1115–1123 (2017)
Turkyilmazoglu, M.: Determination of the correct range of physical parameters in the approximate analytical solutions of non-linear equations using the Adomian decomposition method. Mediterranean J. Math. 13(6), 4019–4037 (2016)
Paripour, M., Hajilou, B.E., Hajilou, A., Heidari, H.: Application of Adomian decomposition method to solve hybrid fuzzy differential equations. J. Taibah Univ. Sci. 9(1), 95–103 (2015)
Kang, S.M.: Improvements in Newton-Raphson method for non-linear equations using modified Adomian decomposition method. Int. J. Math. Anal. 9(39), 1919–1927 (2015)
Bartle, R.G.: Introduction to Real Analysis, 3RD edn. Wiley, New York (2000)
Eggleston, H.G.: Elementary Real Analysis. Cambridge University Press, London (1962)
Abboui, K., Cherruault, Y.: Convergence of Adomians method applied to differential equations. Math. Comput. Mod. 28(5), 103–110 (1994)
Bani Issa, M.S.H., Hamoud, A.: Solving systems of Volterra integro-differential equations by using semi analytical techniques. Technol. Rep. Kansai Univ. 62(03), 685–690 (2020)
Alderemy, A.: Analytical and semi analytical wave solution for longitudinal wave equation via modified auxiliary equation method and Adomian decomposition method, thermal science 23(Suppl. 6), S1943–S1957 (2019)
El-Kalla, I.L.: Convergence of the Adomian method applied to a class of nonlinear integral equations. Appl. Math. Lett. 21, 372–376 (2008)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Rasouli, M., Fariborzi Araghi, M.A. & Damercheli, T. Approximate techniques to solve the partial integro-differential equation arising in operational risk: Adomian decomposition method. Math Sci 17, 43–49 (2023). https://doi.org/10.1007/s40096-021-00438-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40096-021-00438-w