Description: The zeta distribution with regression parameters has been rarely used in statistics because of the difficulty of estimating the parameters by traditional maximum likelihood. This is the abstract of a paper that proposes an alternative method for estimating the parameters based on an iteratively reweighted least-squares algorithm.

Description: The purpose of this paper is to examine a special case of option pricing theory in which the insurance company promises the customer to exercise the option for him. This paper presents a simple formula for valuing the option. From the Actuarial Research Clearing House 1991, Vol.1.

Description: In a recent Society of Actuaries' regional meeting, there was a discussion on an age-old actuarial problem. Within the same company, should the return on equity ROE target vary by profit center depending upon the risk of the profit center? For example, should company management demand a different ROE from the Group Health line than from the Ordinary Life line?

Description: This paper builds on a risk theory model described by Tellenbach [1977]. That model involves Laplace-Stieltjes transforms which pose severe computational difficulties. This paper describes a simple algorithm which appears to work in the special case where the time span considered is reasonably small. The latter condition is typically met if the model refers to cumulative claims. A thorough mathematical treatment of the subject is not even attempted. Rather, the emphasis is on the computational aspect of the problem.

Description: This paper shows the mortality element can be partially isolated allowing an exact annuity value to be readily obtained at any interest rate. From the Actuarial Research Clearing House 1979, Vol.2.

Description: Typically, policyholders do not purchase property/casualty insurance only once in their lifetimes, but make annual decisions concerning insurance purchases. In most personal and commercial lines of insurance, contracts are renewed annually and relationships between insurers and policyholders often include significant past history. To reflect this reality, it would be beneficial to have a theoretical multiple period model of the property/casualty insurance industry. Rothschild and Stiglitz's [1976] one period model of the insurance industry predicts that equilibrium in the marketplace exists in which consumers with differing risk propensities purchase varying amounts of insurance. A multiple period extension of Rothschild and Stiglitz's model can be constructed in which a consumer's future contract choice is contingent on her past contract choice. As in the one period Rothschild-Stiglitz model, a consumer reveals her risk type through the amount of coverage purchased in the period of separation. Since the contract purchased reveals the consumer type, future policies must be conditioned on this information and as such future contracts are contingent on past contracts. Unfortunately, in personal lines of property-casualty insurance, policies are not typically contingent on past policy choices. Future contract provisions, either the amount of insurance offered, or the price of insurance, are usually contingent on the past accident histories of the insureds and not on the amounts of insurance purchased. Two possible reasons given in the literature for this are that contracting insurers cannot restrict the amount of insurance bought from other insurance companies and so the amount cannot be used as a screening mechanism, and that insureds are unaware of their risk type. This paper provides another conjecture as to why these contracts, denoted Rothschild-Stiglitz contracts, are not observed in the market place. Quite simply, the cost of revealing one's type

Description: Up to now, the main aim of credibility theory has been to provide statistical models which allow for estimating [net] risk premiums appropriately. In this note, a simple credibility model based on the percentile principle is introduced. It turns out that there are close connections between the resulting credibility premiums and statistical tolerance limits.

Description: This paper presents a new perspective on three basic financial quantities: assets, liabilities and surplus. The new perspective is developed through a re-examination of the fundamental concepts inherent in these quantities. This re-examination clarifies the difference between the concept and the various rules commonly used to establish their numerical value. With the benefit of this clarification, an alternate approach to the development of surplus is presented. From Actuarial Research Clearing House 1993, VOL. 3.

Description: In estimating mortality rates from the experience of a life insurance company or employee-benefit plan, it is expedient, because of the movement into and out of the covered group on dates other than birthdays or policy anniversaries, to make some assumption about mortality over a fractional part of a year of age. This paper describes and develops the concept of 'exposure' with regard to the more commonly known methods of estimating the rate of mortality, and proposes a fourth methodology. From the Actuarial Research Clearing House 1978, Vol.2.

Description: This paper describes an analysis of data anomalies on computer records on 246 federally-insured mortgages. Twenty-three of the corresponding mortgages were sampled and all were found to have identical amortization plans and to have been insured under the same insurance fund. The question posed, in probabilistic terms, is the following: How many of the remaining 223 mortgages are identical in these two aspects to the 23 sampled mortgages?