A martingale approach to premium calculation principles in an arbitrage free market

Delbaen, Freddy; Haezendonck, J.

doi:10.1016/0167-6687(89)90002-4

Cited by 82 publications

(115 citation statements)

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“…However, the result does not carry over to actuarial valuation in a similar "no-arbitrage" context as introduced by Delbaen and Haezendonck [12]. In fact there are many equivalent probability measures that lead to the same insurance premium.…”

Section: Let Us Assume Thatmentioning

confidence: 84%

“…under which the index remains a compound Poisson process. This subset has been characterized by Delbaen and Haezendonck [12] as follows:…”

Section: Change Of Equivalent Measuresmentioning

confidence: 99%

“…Remark 3 Meister [25] generalized the result of Delbaen and Haezendonck [12] to mixed Poisson and doubly stochastic Poisson processes.…”

Section: Remarkmentioning

confidence: 99%

“…The set of equivalent probability measures that preserve the structure of X has been characterized by Delbaen and Haezendonck [12] and presented in Section 3.2, p. 9 of this paper.…”

Section: Representation Of No-arbitrage Pricesmentioning

confidence: 99%

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Pricing Catastrophe Insurance Derivatives

Muermann

2002

SSRN Journal

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We investigate the valuation of catastrophe insurance derivatives that are traded at the Chicago Board of Trade. By modeling the underlying index as a compound Poisson process we give a representation of no-arbitrage price processes using Fourier analysis. This characterization enables us to derive the inverse Fourier transform of prices in closed form for every fixed equivalent martingale measure. It is shown that the set of equivalent measures, the set of no-arbitrage prices, and the market prices of frequency and jump size risk are in one-to-one connection. Following a representative agent approach we determine the unique equivalent martingale under which prices in the insurance market are calculated.

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Section: Let Us Assume Thatmentioning

confidence: 84%

“…under which the index remains a compound Poisson process. This subset has been characterized by Delbaen and Haezendonck [12] as follows:…”

Section: Change Of Equivalent Measuresmentioning

confidence: 99%

“…Remark 3 Meister [25] generalized the result of Delbaen and Haezendonck [12] to mixed Poisson and doubly stochastic Poisson processes.…”

Section: Remarkmentioning

confidence: 99%

“…The set of equivalent probability measures that preserve the structure of X has been characterized by Delbaen and Haezendonck [12] and presented in Section 3.2, p. 9 of this paper.…”

Section: Representation Of No-arbitrage Pricesmentioning

confidence: 99%

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Pricing Catastrophe Insurance Derivatives

Muermann

2002

SSRN Journal

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“…There also seems to have been an increasingly development speed in the 1990-thies after the important works on dynamic pricing of arbitrage-free (re)insurance markets made by Delbaen and Haezendonck (1989) and Sondermann (1991); see Embrechts (2000) for an exiting overview description. In this paper we will try to describe and unite the headlines of this common theory to a practical understanding and practise in non-life insurance pricing, and thus also try to address some future theoretical challenges.…”

Section: Introductionmentioning

confidence: 99%

Pragmatic insurance option pricing

Holtan¹

2007

Scandinavian Actuarial Journal

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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

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