When uncertainty is associated with some intrinsically relevant states of nature, there is no reason for an agent to base his or her preferences only on probability distribution of claims. We propose a new concept of risk for statecontingent claims that, unlike the standard concept of Rothschild-Stiglitz, does not identify state-contingent claims with their probability distribution. This concep...

∗Odjel za matematiku, Sveučilište u Osijeku, email: [email protected] †Farmeron d.o.o., Osijek, email: [email protected], diplomirana studentica Odjela za matematiku, Sveučilište u Osijeku Danijel Grahovac, Ana Leko Insurance companies have to plan their business so that at any time they have enough capital to pay off the arriving claims. As the claim amounts and the time of their occurren...

Motivation. The paper will address the issue of estimating the uncertainty in the run off of individual large claims in insurance portfolios, which is often the primary source of uncertainty in the reserving risk component of insurance risk. Method. The paper begins by reviewing current methodologies for estimating the uncertainty in loss reserves. Methods until now have focused on aggregate mo...

In non-life insurance, insurers use experience rating to adjust premiums to reflect policyholders’ previous claim experience. Performing prospective experience rating can be challenging when the claim distribution is complex. For instance, insurance claims are semicontinuous in that a fraction of zeros is often associated with an otherwise positive continuous outcome from a right-skewed and lon...

In a non-life insurance business an insurer often needs to build up a reserve to be able to meet his future obligations arising from claims that are known to exist, but for which the actual size is unknown at the time the reserves have to be set. The delay of the actual payment of the claims is, for example, due to long legal procedures or difficulties in determining the size of the claims. The...

Most motor bodily injury (BI) claims are settled by negotiation, with fewer than 5% of cases going to court. A well-defined negotiation strategy is thus very useful for insurance companies. In this paper we assume that the monetary compensation awarded in court is the upper amount to be offered by the insurer in the negotiation process. Using a real database, a log-linear model is implemented t...

We propose two axioms that introduce lower bounds into resource monotonicity requirements for rules for the problem of adjudicating conflicting claims. Suppose the amount to divide increases. The first axiom requires that two claimants whose lower bound changes equally experience an equal change in awards. The second axiom requires that extra resources are divided only among those claimants who...

Bayesian belief networks provide estimates of conditional probabilities, called query responses. The precision of these estimates is assessed using posterior distributions. This paper discusses two claims and a conjecture by Kleiter (1996) concerning the exact posterior distribution of queries. The two claims provide conditions where a query has an exact beta distribution. The first claim is cl...

In this paper, a discrete one-parameter distribution called the semi-Poisson is introduced, which based on set of non-negative integers. It seen that captures over-dispersion and zero-inflation scenarios well. A few properties proposed distribution, such as moments, probability-generating function, index dispersion, recurrence relation for negative moments are presented. The applied to two real...