Does Informational Equivalence Preserve Strategic Behavior? Experimental Results on Trockel’s Model of Selten’s Chain Store Story

The purpose of this study is to experimentally test Trockel’s game, which is a modelling of the classical Chain Store Game (CSG), and determine whether one of the two theories of Equality and Deterrence may better account for the observed behavior. The CSG is an example of a simple game in extensive form where the actual behavior of well-informed players cannot be expected to agree with the clear results of game theoretical reasoning. To explain the disagreement between the theory and the expected behavior, Trockel’s game is proposed as an alternative modelling of the scenario. The existence of more than one equilibrium in Trockel’s game opens a door for reputation building. This study is the first attempt to experimentally test this alternative game with the same purpose. According to my data, there is some evidence in favor of both Equality and Deterrence Hypotheses. However, since the strategies compatible with the Equality Hypothesis are played more frequently, I observe some patterns which share the same intuition with the Deterrence Hypothesis.

Claim Watching and Individual Claims Reserving Using Classification and Regression Trees

We present an approach to individual claims reserving and claim watching in general insurance based on classification and regression trees (CART). We propose a compound model consisting of a frequency section, for the prediction of events concerning reported claims, and a severity section, for the prediction of paid and reserved amounts. The formal structure of the model is based on a set of probabilistic assumptions which allow the provision of sound statistical meaning to the results provided by the CART algorithms. The multiperiod predictions required for claims reserving estimations are obtained by compounding one-period predictions through a simulation procedure. The resulting dynamic model allows the joint modeling of the case reserves, which usually yields useful predictive information. The model also allows predictions under a double-claim regime, i.e., when two different types of compensation can be required by the same claim. Several explicit numerical examples are provided using motor insurance data. For a large claims portfolio we derive an aggregate reserve estimate obtained as the sum of individual reserve estimates and we compare the result with the classical chain-ladder estimate. Backtesting exercises are also proposed concerning event predictions and claim-reserve estimates.

Symplectic mapping class group relations generalizing the chain relation

In this paper, we examine mapping class group relations of some symplectic manifolds. For each [Formula: see text] and [Formula: see text], we show that the [Formula: see text]-dimensional Weinstein domain [Formula: see text], determined by the degree [Formula: see text] homogeneous polynomial [Formula: see text], has a Boothby–Wang type boundary and a right-handed fibered Dehn twist along the boundary that is symplectically isotopic to a product of right-handed Dehn twists along Lagrangian spheres. We also present explicit descriptions of the symplectomorphisms in the case [Formula: see text] recovering the classical chain relation for the torus with two boundary components.

The link between classical reserving and granular reserving through double chain ladder and its extensions

The relationship of the chain ladder method to mathematical statistics has long been debated in actuarial science. During the 1990s it became clear that the originally deterministic chain ladder can be seen as an autoregressive time series or as a multiplicative Poisson model. This paper draws on recent research and concludes that chain ladder can be seen as a structured histogram. This gives a direct link between classical aggregate methods and continuous granular methods. When the histogram is replaced by a smooth counterpart, we have a continuous chain ladder model. Re-inventing classical chain ladder via double chain ladder and its extensions introduces statistically solid approaches of combining paid and incurred data with direct link to granular data approaches. This paper goes through some of the extensions of double chain ladder and introduces new approaches to incorporating and modelling incurred data.

Bayesian over-dispersed Poisson model and the Bornhuetter & Ferguson claims reserving method

We consider the Bayesian over-dispersed Poisson (ODP) model for claims reserving in general insurance. We choose two different types of prior distributions for the parameters and then study the different Bayesian predictors. This study leads, on the one hand, to the classical chain ladder predictor and, on the other hand, to Bornhuetter & Ferguson predictors. We highlight (either analytically or numerically) how these predictors are obtained and how their prediction uncertainty can be determined.