Risk theory refers to a body of techniques to model and measure the risk associated with a portfolio of insurance contracts. A first approach consists in modeling the distribution of total claims over a fixed period of time using the classical collective model of risk theory. A second input of interest to the actuary is the evolution of the surplus of the insurance company over many periods of ...

Risk theory refers to a body of techniques to model and measure the risk associated with a portfolio of insurance contracts. A first approach consists in modeling the distribution of total claims over a fixed period of time using the classical collective model of risk theory. A second input of interest to the actuary is the evolution of the surplus of the insurance company over many periods of ...

In distribution problems, and specifically in bankruptcy issues, the Proportional (P ) and the Egalitarian (EA) divisions are two of the most popular ways to resolve the conflict. Nonetheless, when using the egalitarian division, agents may receive more than her claim. We propose a compromise between the proportional and the egalitarian solutions by considering the restriction that no one recei...

The first method, essentmlly due to GOOVAERTS and DE VYLDER, uses the connection between the probablhty of ruin and the maximal aggregate loss random variable, and the fact that the latter has a compound geometric d lsmbutlon. For the second method, the claim amount distribution is supposed to be a combination of exponential or translated exponential distributions. Then the probablhty of rum ca...

Suppose that, over a fixed time interval of interest, an insurance portfolio generates a random number of independent and identically distributed claims. Under the LCR treaty the reinsurance covers the first l largest claims, while under the ECOMOR treaty it covers the first l − 1 largest claims in excess of the lth largest one. Assuming that the claim sizes follow an exponential distribution o...

Every experimentalist will sooner or later come across a situation in which results from initial "baseline" treatments conform nicely to the Nash equilibrium, but subsequent changes in parameters push the data in ways not predicted by Nash. This may happen when one begins by giving theory its "best shot," reserving stress tests for later. Such tests often involve changing a parameter that, on t...

The paper presents the results of a case study fitting the generalized Pareto distribution to insurance industry claims data. Besides classical parametric procedures, robust statistical concepts are considered. The latter provide instruments to assess the characteristics of estimators also in the neighborhood of parametric models. A demand for robust methods may arise in cases of fitting distri...

Since the beginning of insurance industry, there has been problem fraudulent claims. These are a broad variety illegal activities, most which never uncovered while costing industry billions dollars annually. It is estimated that India's suffering losses around 600–Rs. 600 million each year because growing economy, more awareness, and strengthened distribution networks. 800 crores in sustained y...

We develop a non-life reserving model using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an arbitrary choice of a priori distribution for the ultimate loss. Taking a Bayesian approach to the reserving problem, we derive the process of the conditional distribution of the ultimate loss. The ‘best-estimate ultimate loss process’ is given by the conditional e...

We impose the axiom Independence of Irrelevant Alternatives on division rules for the conflicting claims problem. With the addition of Consistency and Resource Monotonicity, this characterizes a family of rules which can be described in three different but intuitive ways. First, a rule is identified with a fixed monotone path in the space of awards, and for a given claims vector, the path of aw...