Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

This article has no abstract.

Keywords:

actuarial journals;
insurance mathematics;
insurance economics

pdf/insurance-mathematics-and-economics-ira3oq7052.pdf

Insurance: Mathematics and Economics

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Statistics and Computing

This paper argues that most of the problems that actuaries have to deal with in the context of non-life insurance can be usefully cast in the framework of computational intelligence (a.k.a. artificial intelligence), the discipline that studies the design of agents which exhibit intelligent behaviour. Finding an adequate framework for actuarial problems has more than a simply theoretical interest: it also allows a knowledge transfer from the computational intelligence discipline to general insurance, wherever techniques have been developed for problems which are common to both contexts. This has already happened in the past (neural networks, clustering, data mining have all found applications to general insurance) but not systematically, with the result that many useful computational intelligence techniques such as sparsity-based regularisation schemes (a technique for feature selection) are virtually unknown to actuaries.In this first of two papers, we will explore the role of statistical learning in actuarial modelling. We will show that risk costing, which is at the core of pricing, reserving and capital modelling, can be described as a supervised learning problem. Many activities involved in exploratory analysis, such as data mining or feature construction, can be described as unsupervised learning. A comparison of different computational intelligence methods will be carried out, and practical insurance applications (rating factor selection, IBNER analysis) will also be presented.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S1748499512000036

Computational intelligence with applications to general insurance: a review: I – The role of statistical learning

Traditional models of analyzing the general insurance market often focus on the behavior of a single insurer in a competitive market. They assume that the major players in this market are homogeneous and have a common goal to achieve a same long-term business objective, such as solving profit (or utility) maximization. Therefore these individual players in the traditional models can be implemented as a single representative economic agent with full rationality to solve the utility optimization. To investigate insurance pricing (or underwriting) cycles, the existing literature attempts to model various isolated aspects of the market, keeping other factors exogenous. We and that a multi-agent system describing an insurance market affords a helpful understanding of the dynamic interactions of individual agents that is a complementary to the traditional models. Such agent-based models (ABM) try to capture the complexity of the real world. Thus, economic agents are heterogeneous and follow divergent behavioral rules depending on their current unique competitive situations or comparative advantages relating to, for example, their existing market shares, distribution channels, information processes and product differentiations. The real-world continually-evolving environment leads agents to follow common rules of thumb to implement their business strategies, rather than completely be utility-maximizer with perfect foresight in an idealized world. The agents are adaptively learning from their local competition over time. In fact, the insurance cycles are the results of these dynamic interactions of agents in such complex system.

Application of Agent Based Modeling to Insurance Cycles

This paper is an attempt to answer the question “What is the proper framework for understanding risk?” in the context of general insurance. It argues that although actuaries and other risk professionals tend to deal with risk in the context of classical statistics and by resorting to subjective judgment to compensate the inadequacies of this framework, understanding risk is actually an “ecological” problem and it is more fruitful to look at risk in the context of computational intelligence. Computational intelligence (a.k.a. artificial intelligence) is the discipline that deals with designing intelligent agents – agents that are able to learn from data, integrate multiple sources of (often uncertain) knowledge, deal with changes in an environment, make decisions, compete against each other. These are much the same problems that players in the insurance market, whether they be customers, insurers, reinsurers, or the regulator, face daily – and therefore it is quite natural to describe these players as risk agents that have to survive and thrive in an environment (the market). Most actuarial problems, such as pricing, reserving, capital modelling, DFA, pricing optimisation, can be naturally framed as computational intelligence problems. This is not only a theoretical issue: it also allows a technological transfer from the computational intelligence discipline to general insurance, wherever techniques have been developed for problems which are common to both contexts. This has already happened, at least in part, as some computational intelligence techniques such as neural networks, k-means clustering, data mining have found a place in actuarial literature and practice. Others (such as sparsity-based regularisation or dynamic decision networks) are perhaps less familiar to risk professionals, and one of the goals of this paper is indeed to “fill the gaps”, introducing cutting-edge techniques such as the elastic net or spectral clustering to the wider actuarial community. In this paper, computational intelligence techniques are always illustrated through simple insurance applications and are systematically compared to one another to determine their adequacy to our needs: regularisation, neural networks and generalised linear modelling are compared as tools for predictive modelling; fuzzy set theory and Bayesian analysis are compared as tools for dealing with uncertain and soft knowledge; dynamic Bayesian networks and Kalman filtering are compared as tools to understand changes in the environment; and so on. Apart from the methodological findings, some practical recommendations also emerge from this investigation: (i) that the use of regularisation techniques should be expanded in actuarial practice, as these solve the problem of variable selection efficiently; (ii) that cross-validation and the Bayesian Information Criterion should be used for model validation alongside more traditional methods such as the Akaike Information Criterion and the holdout sample method, especially in situations where data is scant; (iii) that Bayesian analysis should be the preferred tool for dealing with data uncertainty, model uncertainty and soft knowledge (rather than fuzzy set theory or rule-based systems), and that Bayesian networks should be used where we have complex chains of dependency; (iv) that dynamic Bayesian networks are a more general alternative to Kalman filtering (applied in the past to reserving and pricing) to deal with environment changes, and can also be extended to incorporate decisions and utility (dynamic decision networks), allowing to deal with problems such as DFA and pricing optimisation; (v) that multiagent systems may be used to simulate markets and design optimal strategies in the face of competition, or to design regulation that achieves some overall goal. In all these techniques, the Bayesian framework is ubiquitous. Computational intelligence techniques are powerful and (unlike artificial intelligence in the 70s or 80s) are now on a more rigorous basis. However, there are some obvious limitations, which boil down to the failing of artificial intelligence to achieve its goals stated in the early manifestos in the 1960s and beyond: that of producing agents which exhibited truly intelligent behaviour. None of the techniques above truly replace human judgment, but rather support it and enhance our ability to justify decisions quantitatively. A, when they are used for prediction they work only when the environment exhibits some sort of stationarity – and the non-stationarity introduced by humans changing the rules of the game is especially difficult to tackle. Finally, some of the techniques – especially those involving multiple agents – are so complex and rich in variables that they often offer only a formal, rather than practical, solution.

/pdf/computational-intelligence-techniques-for-general-insurance-5gk9xrf3g4.pdf

Computational intelligence techniques for general insurance

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Computational intelligence techniques for general insurance