Pricing optional group term insurance: a new approach using reservation prices

Consider an employer who, through an insurer, provides optional group term life insurance to a group of employees. The employees are assumed to have mortality following a mixture mortality model where they have different mortality rates belonging to a common probability distribution. To reduce the effects of possible adverse selection, the insurer sets a maximum acceptable mortality level (qM). The insurer then uses a costly medical underwriting/exam to determine each applicant's mortality level, q. If q>qM the employee is refused insurance otherwise insurance is granted. Each employee is assumed to have a reservation price for term insurance. Economic theory is used to determine the employees' inverse aggregate demand function. This demand function is then used to determine the mortality cut-off level and premium that maximize the insurer's expected profits. First order conditions and several necessary conditions for profit maximization are given.