Application of the radial basis function in solving an operational risk management model: investigating the probability of bank survival with risk reserves

Operational risk is one of the influential risks identified by banking practitioners, and as the international banking supervisor, the Basel Committee on Banking Supervision has paid special attention to it. There are various methods for measuring and managing this type of banking risk (eg, the advanced measurement approach). Using the radial basis function approach, we compute the probability of bank survival using a partial Volterra integrodifferential equation. Given the importance of operational risk in financial institutions, especially banks, we examine a mathematical model of this risk and solve it using numerical methods. Also, by considering the impact of the bank’s probability of survival on the amount of risk reserves, we investigate the effect of fluctuation in risk reserves on the probability of survival of an organization. To complete the investigation, we calculated the amount of risk storage required to achieve the desired probability of survival.