Net Single Premium Research Articles

Pricing long term care insurance contracts

Insurance companies are faced with the problem of pricing Long Term Care (LTC) insurance contracts. An LTC contract provides the insured benefits should he become in need of care. We consider several models describing the changes in the needs, of the insured, for care over time. Some models are more conservative than others, some are based on ADL's and one model assumes alternating periods of activity and disability. A quite general Markovian multistate model is also analyzed. A basic concept needed for pricing LTC contracts is the r.v. Discounted Value of Future Benefits (DVFB). Using the expected DVFB, termed elsewhere net single premium, we find the annual premiums for all the models. The methods used to price the contracts include Markov chain analysis, potential theoretic approach, backward induction and Bellman's equation of dynamic programming.

The optimality of the net single premium in life insurance

Vadiveloo et al (1982) introduced a criterion for choosing, among the various net risk premium payment plans, the so-called optimum one. They considered a life insurance situation where benefits were payable at the end of the year of death. Of course, premiums cease after death! This optimum criterion was the minimization of the discounted net profit variance. Their model can be mathematically described as follows. Consider an insured life aged exactly x having a death benefit with present value, if death occurs at time t, denoted by B(t). If the present value of the total premiums paid up to time t is R(t) and the random variable T denotes the time of the death of x, then the profit at death has present value Z(T) where Z(T)=R(T)−B(T).The optimum net premium payment plan, R*(t), is the one that minimizes Var[Z(T)] subject to E[Z(T)] = 0.

The Rate of Return on Life Insurance and Annuities

Net single premium life insurance and annuity contracts can be regarded as investments with corresponding internal rates of return. Since the time until death of the policyholder is a random variable, so must be the internal rate generated on the contract. Aspects of the distribution of the internal rate are investigated for standard life insurance and annuity contracts.

Single premium for an assurance of the amount outstanding under a Building Society mortgage.

The accurate calculation of the net single premium at rate of interestifor an assurance to cover the amount outstanding under a Building Society Mortgage subject to a higher rate of interestjis a fairly lengthy process. However, as a fairly heavy contingency loading is usually added, the following simple method gives results sufficiently accurate for most practical purposes.For a loan of initial amount unity repayable overnyears by level annual instalments in arrear the single premium calculated at rate of interestjon a life agexis given by the expressionThe sum assured is payable at the end of the year of death and is equal to the amount of the loan then outstanding before payment of the instalment then due.