Premium Calculation on the Restricted Parameter Spaces

Premium for a certain portfolio can be estimated differently from: (1) an insurer and a policyholder's viewpoint; and (2) theoretical or practical viewpoints, say p1 and p2. Now, the natural question is which estimator shows more appropriate premium in an interval [p1, p2]. This paper employs the concept of demand function along with reservation price to answer the above question. Namely, it: (1) extends definition of the reservation price from an insurer's viewpoint by employing the concept of demand function; and (2) develops an elegant technique to estimate uniquely, a premium p, say equivalent premium, from an interval [p1, p2], such that the utility ratios for both the insurer and the policyholder be equivalent. Applications are given for the life insurance and insurance portfolios with diffusion or Poisson risk processes