This paper deals with theoretical and practical pricing of non-life insurance contracts within a financial option pricing context. The market based assumption approach of the option context fits well into the practical nature of non-life insurance pricing and valuation. Basic facts in most insurance markets like the existence of quite different insurer price offers on the same claims risk in the same market, support the need for this approach. The paper outlines insurance and option pricing in a parallel setup. First it takes a complete market approach, focusing dynamic hedging, no-arbitrage and risk-neutral martingale valuation principles within insurance and options. Secondly it takes an incomplete market view by introducing supply and demand effects via purchasing preferences in the market. Finally the paper discusses pragmatic insurance price models, parameter estimation techniques and international best practice of insurance pricing. The overall aim of the paper is to describe and unite the headlines of the more or less common insurance and option price theory, and hence increase the pragmatic understanding of this theory from a business point of view. KeywordsInsurance and financial option contracts; insurance and option pricing theory; complete and incomplete markets; dynamic hedging and no-arbitrage; risk-neutral martingales; purchasing preferences; risk, cost and market price adjustments; parameter estimation; pragmatic and best practice pricing.2
The paper introduces an alternative approach to the traditional experience rating theory in automobile insurance. The approach is based on a simple theory of how high deductibles financed by loans maintain the risk differentiation in an automobile insurance arrangement. Thus the approach differs totally from the usual bonus-malus classes as well as from the credibility based experience rating ideas. The paper is of a theoretical nature and leads up to a mathematical description of how the approach may be optimalized within the framework of a risk model. KEYWORDSBonus-malus systems; optimal deductibles financed by loans. BACKGROUNDFrom a practical point of view it is well-known that the existing automobile bonus-malus systems possess several considerable disadvantages which are difficult, or even impossible, to handle within the traditional theory of experience rating. The aim of this paper is to introduce an alternative bonus-malus approach which, at least theoretically, eliminates the most important ones of these disadvantages. CRITICISM OF EXISTING BONUS SYSTEMSTo motivate the new bonus-malus (B-M) approach it is appropriate to stress the usual criticism of the existing B-M systems. In particular, the existing systems are, among other things, based on two general characteristics:(i) The claim amounts are omitted as a posterior tariff criterion, (ii) At any time the policyholders may leave an insurance company without any further financial commitments to the company.These characteristics lead to three of the most considerable disadvantages:(2.1) Regarding an occurred claim, the future loss of bonus will in many cases exceed the claim amount.1 An earlier version of this work has been presented at the ASTIN Colloquium, Stockholm 1991. ASTIN BULLETIN, Vol. 24. No. 1, 1994 Because only the number of claims (and of course the discount rate) in an insurance period determines the premium in the following period, it follows that (2.1) is an immediate consequence of (i). In many cases (2.1) gives the policyholder a feeling of unfairness, especially if the loss of bonus is much higher than the occurred claim amount. A consequence of this is the wellknown bonus hunger behaviour of the policyholders.Disadvantage (2.2) is of course a consequence of (ii). Malus evaders let the remaining policyholders pay the bill for their (the evaders') claim costs. This has, at least in Norway, been a serious problem in the insurance industry, mainly because of an unsatisfactory exchange of bonus information between the insurance companies.Because all insurance arrangements attached to existing B-M systems are exposed to bonus hunger as well as malus evasion, it follows that (2.3) is a secondary consequence of (2.1) and (2.2). A higher average rate of discount is contrary to risk differentiation, which is the objective of all B-M systems. In an extreme situation the result might be that the great majority of the policyholders are at, or close to, the maximum rate of discount.A number of authors have focused on the disadvantages...
The paper analyses the questions: Should -or should not -an individual buy insurance? And if so, what insurance coverage should he or she prefer? Unlike classical studies of optimal insurance coverage, this paper analyses these questions from a bonus-malus point of view, that is, for insurance contracts with individual bonus-malus (experience rating or no-claim) adjustments. The paper outlines a set of new statements for bonus-malus contracts and compares them with corresponding classical statements for standard insurance contracts. The theoretical framework is an expected utility model, and both optimal coverage for a fixed premium function and Pareto optimal coverage are analyzed. The paper is an extension of another paper by the author, see Holtan (2001), where the necessary insight to -and concepts of -bonus-malus contracts are outlined.
The paper analyses the question: Should an insurance customer carry an occurred loss himself, or should he make a claim to the insurance company? This question is important within bonus-malus contracts with individual experience adjustments of the premium. The analysis model includes a bonus hunger strategy where the customers prefer the most profitable financial alternative, that is, the alternative which represents the lowest rate of interest. Hence the loss of bonus after a claim is calculated as a rate of interest paid from the customer to the insurer. Within this model the paper outlines the existence of a true compensation function and a relative cost function for each customer. A set of properties for bonus-malus contracts are presented and discussed. A concrete example of a bonus-malus system and an insurance compensation function illustrates the theoretical framework in a practical manner.
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