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11 - Spatial Modeling
- from II - Predictive Modeling Methods
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- By Eike Brechmann, Technische Universität München, Claudia Czado, Technische Universitat in Munich
- Edited by Edward W. Frees, University of Wisconsin, Madison, Richard A. Derrig, Temple University, Philadelphia, Glenn Meyers
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- Book:
- Predictive Modeling Applications in Actuarial Science
- Published online:
- 05 August 2014
- Print publication:
- 28 July 2014, pp 260-279
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Summary
Chapter Preview. This chapter presents statistical models that can handle spatial dependence among variables. Spatial dependence refers to the phenomenon that variables observed in areas close to each other are often related. Ignoring data heterogeneity due to such spatial dependence patterns may cause overdispersion and erroneous conclusions. In an actuarial context, it is important to take spatial information into account in many cases, such as in the insurance of buildings threatened by natural catastrophes; in health insurance, where diseases affect specific regions; and also in car insurance, as we discuss in an application.
In particular, we describe the most common spatial autoregressive models and show how to build a joint model for claim severity and claim frequency of individual policies based on generalized linear models with underlying spatial dependence. The results show the importance of explicitly considering spatial information in the ratemaking methodology.
Introduction
It is important to take spatial information related to insurance policies into account when predicting claims and ratemaking. The most prominent example is the modeling of natural catastrophes needed for the insurance of buildings. Another example is health insurance, where spatial information is relevant for an accurate assessment of the underlying risks, because frequencies of some diseases may vary by region. Frequencies in neighbor regions are often expected to be more closely related than those in regions far from each other. This phenomenon is usually referred to as spatial dependence.
6 - Statistical Assessments of Systemic Risk Measures
- from PART II - STATISTICS AND SYSTEMIC RISK
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- By Carole Bernard, University of aterloo, Eike Christian Brechmann, Technische Universität München, Claudia Czado, Universität München
- Edited by Jean-Pierre Fouque, University of California, Santa Barbara, Joseph A. Langsam, University of Maryland, College Park
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- Book:
- Handbook on Systemic Risk
- Published online:
- 05 June 2013
- Print publication:
- 23 May 2013, pp 165-179
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Summary
Abstract In this chapter, we review existing statistical measures for systemic risk and discuss their strengths and weaknesses. Among them we discuss the Conditional Value-at-Risk (CoVaR) introduced by Adrian and Brunnermeier (2010) and the Systemic Expected Shortfall (SES) of Acharya, Pedersen, Philippon and Richardson (2011). As systemic risk is highly related to financial contagion, we will explain the drawbacks and advantages of looking at “coexceedances” (simultaneous extreme events) or at the local changes in “correlation” that have been proposed in the literature on financial contagion (Bae, Karolyi and Stulz (2003), Baig and Goldfajn (1999) and Forbes and Rigobon (2002)).
Introduction and background on systemic risk
During the financial crisis of 2007–2009, worldwide taxpayers had to bailout many financial institutions. Governments are now trying to understand why the regulation failed, why capital requirements were not enough and how a guaranty fund should be built to address the next financial crisis. To implement such a fund, one needs to understand the risk that each institution represents to the financial system and why regulatory capital requirements were not enough. In the financial and insurance industry, capital requirements have the following common properties. First, they depend solely on the distribution of the institution's risk and not on the outcomes in the different states of the world. Second, capital requirements and marginal calculations treat each institution in isolation. An important element is missing in the above assessment of risk: it is the dependency between the individual institution and the economy or the financial system. The regulation should “be regulating each bank as a function of both its joint (correlated) risk with other banks as well as its individual (bank-specific) risk” (Acharya (2009)).