Insurance with multiple insurers: A game-theoretic approach

This paper studies the set of Pareto optimal insurance contracts and the core of an insurance game. Our setting allows multiple insurers with translation invariant preferences. We characterise the Pareto optimal contracts, which determines the shape of the indemnities. Closed-form and numerical solutions are found for various preferences that the insurance players might have. Determining associated premiums with any given optimal Pareto contract is another problem for which economic-based arguments are further discussed. We also explain how one may link the recent fast growing literature on risk-based optimality criteria to the Pareto optimality criterion and we show that the latter is much more general than the former one, which according to our knowledge, has not been pointed out by now. Further, we extend some of our results when model risk is included, i.e. there is some uncertainty with the risk model and/or the insurance players make decisions based on divergent beliefs about the underlying risk. These robust optimal contracts are investigated and we show how one may find robust and Pareto efficient contracts, which is a key decision-making problem under uncertainty

A conodont fauna of the Dinantian from the Kuznetsk Basin (Southern Siberia)

Lower to middle Tournaisian conodonts are recorded for the first time from southern Siberia. An exact correlation with Belgian and West-German Tournaisian stratotypes seems impossible. The conodont assemblage is characteristic of shallow marine costal areas

Nash Equilibria in Optimal Reinsurance Bargaining

We introduce a strategic behavior in reinsurance bilateral transactions, where agents choose the risk preferences they will appear to have in the transaction. Within a wide class of risk measures, we identify agents' strategic choices to a range of risk aversion coefficients. It is shown that at the strictly beneficial Nash equilibria, agents appear homogeneous with respect to their risk preferences. While the game does not cause any loss of total welfare gain, its allocation between agents is heavily affected by the agents' strategic behavior. This allocation is reflected in the reinsurance premium, while the insurance indemnity remains the same in all strictly beneficial Nash equilibria. Furthermore, the effect of agents' bargaining power vanishes through the game procedure and the agent who gets more welfare gain is the one who has an advantage in choosing the common risk aversion at the equilibrium.Comment: 22 pages, 3 figure

Forecasting compositional risk allocations

We analyse models for panel data that arise in risk allocation problems, when a given set of sources are the cause of an aggregate risk value. We focus on the modelling and forecasting of proportional contributions to risk over time. Compositional data methods are proposed and the time-series regression is flexible to incorporate external information from other variables. We guarantee that projected proportional contributions add up to 100%, and we introduce a method to generate confidence regions with the same restriction. An illustration is provided for risk capital allocations

COMPREHENSION & VISUALIZATION - Teaching Students to Solve Word Problems

ABSTRACT In this feasibility study the authors describe and evaluate a word problem solving instruction, based on the principles underlying instructional programs like Solve it! and schema-based instruction. This instruction is executed during a five-week intervention period in a group of four less successful second grade word problem solvers. The effectiveness of the word problem solving instruction is reported by means of students' performances on combine, change and compare problems before and after the intervention period, as well as by examining whether they executed the solution steps of the instruction correctly. This feasibility study provides important insights with regard to varying ways in which a word problem solving instruction can influence the solution strategies and performances of students who perform poorly on word problems. WORD PROBLEM SOLVING PROCESS Look at the following example of a word problem [Word problem example] "Mary has 9 marbles. She has 4 marbles more than John. How many marbles does John have?" Tim, a seven-year-old boy who is in the second grade of elementary school, has difficulties with solving word problems like the one that is given in the example above. While solving these word problems, Tim often uses an impulsive, superficial solution strategy. Significantly, he only focuses on selecting the presented numbers (9 and 4) and identifying the relational keywords (more than), which subsequently form the basis for his mathematical calculations. Tim's strategy often leads to an incorrect answer to the word problem. In this situation, Tim performed an addition operation where a subtraction operation was required, that is 9 + 4 = 13 instead of 9 -4 = 5. The incorrect answer is not the result of a lack of calculation ability, but a result of a problem with deeply and correctly understanding the word problem text. Mathematical word problem solving plays a prominent role in the curriculum of contemporary approaches to teaching mathematics [1

ASAS/WHO ICF Core Sets for ankylosing spondylitis (AS): how to classify the impact of AS on functioning and health

Objective: To report on the results of a standardised consensus process agreeing on concepts typical and/or relevant when classifying functioning and health in patients with ankylosing spondylitis (AS) based on the International Classification of Functioning and Health (ICF).Methods: Experts in AS from different professional and geographical backgrounds attended a consensus conference and were divided into three working groups. Rheumatologists were selected from members of the Assessment of SpondyloArthritis international Society (ASAS). Other health professionals were recommended by ASAS members. The aim was to compose three working groups with five to seven participants to allow everybody's contribution in the discussions. Experts selected ICF categories that were considered typical and/or relevant for AS during a standardised consensus process by integrating evidence from preceding studies in alternating working group and plenary discussions. A Comprehensive ICF Core Set was selected for the comprehensive classification of functioning and a Brief ICF Core Set for application in trials.Results: The conference was attended by 19 experts from 12 countries. Eighty categories were included in the Comprehensive Core Set, which included 23 Body functions, 19 Body structures, 24 Activities and participation and 14 Environmental factors. Nineteen categories were selected for the Brief Core Set, which included 6 Body functions, 4 Body structures, 7 Activities and participation and 2 Environmental factors.Conclusion: The Comprehensive and Brief ICF Core Sets for AS are now available and aim to represent the external reference to define consequences of AS on functioning

Genetic fuzzy system predicting contractile reactivity patterns of small arteries

Monitoring of physiological surrogate end points in drug development generates dynamic time-domain data reflecting the state of the biological system. Conventional data analysis often reduces the information in these data by extracting specific data points, thereby discarding potentially useful information. We developed a genetic fuzzy system (GFS) algorithm that is capable of learning all information in time-domain physiological data. Data on isometric force development of isolated small arteries were used as a framework for developing and optimizing a GFS. GFS performance was improved by several strategies. Results show that optimized fuzzy systems (OFSs) predict contractile reactivity of arteries accurately. In addition, OFSs identified significant differences that were undetectable using conventional analysis in the responses of arteries between groups. We concluded that OFSs may be used in clustering or classification tasks as aids in the objective identification or prediction of dynamic physiological behavior

Risk-Sharing and Contingent Premia in the Presence of Systematic Risk: The Case Study of the UK COVID-19 Economic Losses

Motivated by macroeconomic risks, such as the COVID-19 pandemic, we consider different risk management setups and study efficient insurance schemes in the presence of low probability shock events that trigger losses for all participants. More precisely, we consider three platforms: the risk-sharing, insurance and market platform. First, we show that under a non-discriminatory insurance assumption, it is optimal for everybody to equally share all risk in the market. This gives rise to a new concept of a contingent premium which collects the premia ex-post after the losses are realised. Insurance is then a mechanism to redistribute wealth, and we call this a risk-sharing solution. Second, we show that in an insurance platform, where the insurance is regulated, the tail events are not shared, but borne by the government. Third, in a competitive market we see how a classical solution can raise the risk of insolvency. Moreover, in a decentralised market, the equilibrium cannot be reached if there is adequate sensitivity to the common shock events. In addition, we have applied our theory to a case where the losses are calibrated based on the UK Coronavirus Job Retention Scheme

Comparison of organic and conventional dairy farm economic and environmental performances throughout North West Europe

From an environmental point of view, organic farming (OF) systems have been identified as beneficial thanks to a system allowing fewer losses of nitrogen (N) per ha and lower green house gases (GHG) emissions per ha and per ton of milk (TM). From an economic point of view, milk coming from these OF systems is sold at a higher prize. However, incomes provided by both systems are similar (for similar amount of milk produced). This may be explained by higher input costs per unit of product for OF systems and by more incomes coming from sold crops for conventional farming (CF) systems. Therefore, on the one hand CF systems may improve their environmental performances by reducing the amount of inputs brought into the system, for example through a better forage and fertilisation management. On the other hand, the valorisation of milk through a differentiated production or market (price premium due to a label and/or on-farm transformation and/or sale) may bring them higher incomes. OF system may increase their incomes by selling one cash crop destined for human consumption and by finding the good balance between intensivity and extensivity in order to better valorise the inputs brought into the system

Matching commercial thrips predating phytoseids with the highly diversified climatic conditions of different strawberry production systems

Flower inhabiting thrips (Order: Thysanoptera) are a major threat to fruit quality in strawberry production around the world. As chemical control is often inefficient, alternative control measures are of broad and current interest. Their fast reproduction makes predatory mites highly suitable for thrips control in a crop with a relatively short cropping season like strawberry. However, climatic conditions of strawberry production can differ strongly depending on the production system (glasshouse, plastic tunnel, open field, etc.) and the time span of cultivation (depending mostly on planting date and the type of cultivar: summer-or everbearing). As predatory mites typically display a temperature-dependent life history and the current commercially available thrips predating phytoseids vary in geographic origin, one can assume that under certain climatic conditions some species will be more applicable than others. The goal of this study is to determine which species are suitable for which climatic conditions. Therefore all (Belgian) production systems and time spans are categorized into three climate types, simulated in the laboratory. The population build-up of seven predatory mite species (A. degenerans, A. montdorensis, A. andersoni, A. limonicus, A. swirskii, N. cucumeris and E. gallicus) were assessed for each of these climatic conditions. Under the coldest condition (A), the in West-Europe indigenous E. gallicus was the only species with a significant population build up. When moderate conditions (B) were simulated E. gallicus, N. cucumeris and A. limonicus were most successful. The warmest regime (C) was most adequate for E. gallicus and A. swirskii