Calculation of optimum premium values

Abstract

The present paper deals with optimizing the maximum premium values using Hamiltonian-Jacobi-Bellamann equation. Here it is considering that quadratic and fractional power utility functions for different loss distributions of discrete analogues of continuous distributions. It has been seen that the quadratic utility function is more beneficial to the insured and the fractional power utility function is more beneficial to insurer. Numerical illustrations for discrete analogues of continuous distributions using these two utility functions are given.