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In this contribution, the upper bounds for sums of dependent random variables X1 + X2 +...+ Xn derived by using comonotonicity are sharpened for the case when there exists a random variable Z such that the distribution functions of the Xi, given Z = z, are known. By a similar technique, lower...
Persistent link: https://www.econbiz.de/10014059600
Risk measures have been studied for several decades in the actuarial literature, where they appeared under the guise of premium calculation principles. Risk measures and properties that risk measures should satisfy have recently received considerable attention in the financial mathematics...
Persistent link: https://www.econbiz.de/10012734584
In an insurance context, one is often interested in the distribution function of a sum of random variables. Such a sum appears when considering the aggregate claims of an insurance portfolio over a certain reference period. It also appears when considering discounted payments related to a single...
Persistent link: https://www.econbiz.de/10012708263
Many types of insurance premium principles and/or risk measures can be characterized by means of a set of axioms, which in many cases are rather arbitrarily chosen and not always in accordance with economic reality. In the present paper we gener alize Yaari's risk measure by relaxing his axioms....
Persistent link: https://www.econbiz.de/10012761697
In this paper, we investigate the relationship between comonotonicity and stoploss order. We prove our main results by using a characterization of stop-loss order within the framework of Yaari's (1987) dual theory of choice under risk. Wang and Dhaene (1997) explore related problems in the case...
Persistent link: https://www.econbiz.de/10012761737
We consider the problem of determining appropriate solvency capital requirements for an insurance company or a financial institution. We demonstrate that the subadditivity condition that is often imposed on solvency capital principles can lead to the undesirable situation where the shortfall...
Persistent link: https://www.econbiz.de/10012764416
Knowledge of the distribution function of the stochastically compounded value of a series of future (positive and/or negative) payments is needed for solving several problems in an insurance or finance environment, see e.g. Dhaene et al. (2002 a,b). In Kaas et al. (2000), convex lower bound...
Persistent link: https://www.econbiz.de/10012767393
In this paper we examine and summarize properties of several well-known risk measures that can be used in the framework of setting solvency capital requirements for a risky business. Special attention is given to the class of (concave) distortion risk measures. We investigate the relationship...
Persistent link: https://www.econbiz.de/10012767394
We consider the problem of how to determine the required level of the current provision in order to be able to meet a series of future deterministic payment obligations, in case the provision is invested according to a given random return process. Approximate solutions are derived, taking into...
Persistent link: https://www.econbiz.de/10012767416
In this paper we give some methods to set up confidence bounds for the discounted IBNR reserve. We start with a loglinear regression model and estimate the parameters by maximum likelihood such as given for example in Doray, 1996. The knowledge of the distribution function of the discounted IBNR...
Persistent link: https://www.econbiz.de/10012780839