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Risks, Volume 2, Issue 4 (December 2014), Pages 393-488

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Editorial

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Open AccessEditorial Special Issue on Risk Management Techniques for Catastrophic and Heavy-Tailed Risks
Risks 2014, 2(4), 467-468; doi:10.3390/risks2040467
Received: 4 November 2014 / Accepted: 5 November 2014 / Published: 14 November 2014
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Abstract
The publication of several special issues was part of the initiatives taken in 2013 to launch Risks as a new online journal. It seemed natural to devote one to this important, concrete and complex problem of managing catastrophic and heavy tailed risks. We
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The publication of several special issues was part of the initiatives taken in 2013 to launch Risks as a new online journal. It seemed natural to devote one to this important, concrete and complex problem of managing catastrophic and heavy tailed risks. We received an enthusiastic response last spring to the call for invited and contributed research papers and are proud of the special issue now being published. The emphasis was put on quality rather than quantity; this special issue contains three invited and two contributed research papers. Full article
(This article belongs to the Special Issue Risk Management Techniques for Catastrophic and Heavy-Tailed Risks)

Research

Jump to: Editorial

Open AccessArticle Tail Risk in Commercial Property Insurance
Risks 2014, 2(4), 393-410; doi:10.3390/risks2040393
Received: 6 April 2014 / Revised: 26 July 2014 / Accepted: 30 July 2014 / Published: 29 September 2014
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Abstract
We present some new evidence on the tail distribution of commercial property losses based on a recently constructed dataset on large commercial risks. The dataset is based on contributions from Lloyd’s of London syndicates, and provides information on over three thousand claims occurred
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We present some new evidence on the tail distribution of commercial property losses based on a recently constructed dataset on large commercial risks. The dataset is based on contributions from Lloyd’s of London syndicates, and provides information on over three thousand claims occurred during the period 2000–2012, including detailed information on exposures. We use occupancy characteristics to compare the tail risk profiles of different commercial property exposures, and find evidence of substantial heterogeneity in tail behavior. The results demonstrate the benefits of aggregating granular information on both claims and exposures from different data sources, and provide warning against the use of reserving and capital modeling approaches that are not robust to heavy tails. Full article
(This article belongs to the Special Issue Risk Management Techniques for Catastrophic and Heavy-Tailed Risks)
Open AccessArticle Measuring Risk When Expected Losses Are Unbounded
Risks 2014, 2(4), 411-424; doi:10.3390/risks2040411
Received: 26 May 2014 / Revised: 5 September 2014 / Accepted: 10 September 2014 / Published: 30 September 2014
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Abstract
This paper proposes a new method to introduce coherent risk measures for risks with infinite expectation, such as those characterized by some Pareto distributions. Extensions of the conditional value at risk, the weighted conditional value at risk and other examples are given. Actuarial
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This paper proposes a new method to introduce coherent risk measures for risks with infinite expectation, such as those characterized by some Pareto distributions. Extensions of the conditional value at risk, the weighted conditional value at risk and other examples are given. Actuarial applications are analyzed, such as extensions of the expected value premium principle when expected losses are unbounded. Full article
(This article belongs to the Special Issue Risk Management Techniques for Catastrophic and Heavy-Tailed Risks)
Open AccessArticle A Note on the Fundamental Theorem of Asset Pricing under Model Uncertainty
Risks 2014, 2(4), 425-433; doi:10.3390/risks2040425
Received: 13 May 2014 / Revised: 22 August 2014 / Accepted: 28 September 2014 / Published: 10 October 2014
Cited by 2 | PDF Full-text (236 KB) | HTML Full-text | XML Full-text
Abstract
We show that the recent results on the Fundamental Theorem of Asset Pricing and the super-hedging theorem in the context of model uncertainty can be extended to the case in which the options available for static hedging (hedging options) are quoted with bid-ask
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We show that the recent results on the Fundamental Theorem of Asset Pricing and the super-hedging theorem in the context of model uncertainty can be extended to the case in which the options available for static hedging (hedging options) are quoted with bid-ask spreads. In this set-up, we need to work with the notion of robust no-arbitrage which turns out to be equivalent to no-arbitrage under the additional assumption that hedging options with non-zero spread are non-redundant. A key result is the closedness of the set of attainable claims, which requires a new proof in our setting. Full article
Open AccessArticle A Markov Chain Model for Contagion
Risks 2014, 2(4), 434-455; doi:10.3390/risks2040434
Received: 22 September 2014 / Revised: 27 October 2014 / Accepted: 29 October 2014 / Published: 5 November 2014
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Abstract
We introduce a bivariate Markov chain counting process with contagion for modelling the clustering arrival of loss claims with delayed settlement for an insurance company. It is a general continuous-time model framework that also has the potential to be applicable to modelling the
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We introduce a bivariate Markov chain counting process with contagion for modelling the clustering arrival of loss claims with delayed settlement for an insurance company. It is a general continuous-time model framework that also has the potential to be applicable to modelling the clustering arrival of events, such as jumps, bankruptcies, crises and catastrophes in finance, insurance and economics with both internal contagion risk and external common risk. Key distributional properties, such as the moments and probability generating functions, for this process are derived. Some special cases with explicit results and numerical examples and the motivation for further actuarial applications are also discussed. The model can be considered a generalisation of the dynamic contagion process introduced by Dassios and Zhao (2011). Full article
Open AccessArticle A Duality Result for the Generalized Erlang Risk Model
Risks 2014, 2(4), 456-466; doi:10.3390/risks2040456
Received: 18 September 2014 / Revised: 21 October 2014 / Accepted: 27 October 2014 / Published: 6 November 2014
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Abstract
In this article, we consider the generalized Erlang risk model and its dual model. By using a conditional measure-preserving correspondence between the two models, we derive an identity for two interesting conditional probabilities. Applications to the discounted joint density of the surplus prior
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In this article, we consider the generalized Erlang risk model and its dual model. By using a conditional measure-preserving correspondence between the two models, we derive an identity for two interesting conditional probabilities. Applications to the discounted joint density of the surplus prior to ruin and the deficit at ruin are also discussed. Full article
Open AccessArticle Worst-Case Portfolio Optimization under Stochastic Interest Rate Risk
Risks 2014, 2(4), 469-488; doi:10.3390/risks2040469
Received: 9 October 2014 / Revised: 11 November 2014 / Accepted: 14 November 2014 / Published: 1 December 2014
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Abstract
We investigate a portfolio optimization problem under the threat of a market crash, where the interest rate of the bond is modeled as a Vasicek process, which is correlated with the stock price process. We adopt a non-probabilistic worst-case approach for the height
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We investigate a portfolio optimization problem under the threat of a market crash, where the interest rate of the bond is modeled as a Vasicek process, which is correlated with the stock price process. We adopt a non-probabilistic worst-case approach for the height and time of the market crash. On a given time horizon [0; T], we then maximize the investor’s expected utility of terminal wealth in the worst-case crash scenario. Our main result is an explicit characterization of the worst-case optimal portfolio strategy for the class of HARA (hyperbolic absolute risk aversion) utility functions. Full article

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