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Risk Finance for Catastrophe Losses with Pareto-Calibrated Lévy-Stable Severities

Authors

  • Michael R. Powers,

    Corresponding author
      Michael R. Powers, Department of Finance, School of Economics and Management, Tsinghua University, 386G Weilun Building, Beijing 100084, China; tel: 8601-62767253; powers@sem.tsinghua.edu.cn or michael.powers@temple.edu.
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    • Department of Finance, School of Economics and Management, Tsinghua University, 386G Weilun Building, Beijing 100084, China.

    • Department of Risk Management and Insurance, Fox School of Business, Temple University.

    • The author is on leave from the Fox School of Business, Temple University.

  • Thomas Y. Powers,

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    • Department of Economics, Harvard University and Harvard Business School.

  • Siwei Gao

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    • Department of Risk Management and Insurance, Fox School of Business, Temple University.

    • Department of Accounting, Finance, and Information Systems, Insurance Program, Eastern Kentucky University.


Michael R. Powers, Department of Finance, School of Economics and Management, Tsinghua University, 386G Weilun Building, Beijing 100084, China; tel: 8601-62767253; powers@sem.tsinghua.edu.cn or michael.powers@temple.edu.

Abstract

For catastrophe losses, the conventional risk finance paradigm of enterprise risk management identifies transfer, as opposed to pooling or avoidance, as the preferred solution. However, this analysis does not necessarily account for differences between light- and heavy-tailed characteristics of loss portfolios. Of particular concern are the decreasing benefits of diversification (through pooling) as the tails of severity distributions become heavier. In the present article, we study a loss portfolio characterized by nonstochastic frequency and a class of Lévy-stable severity distributions calibrated to match the parameters of the Pareto II distribution. We then propose a conservative risk finance paradigm that can be used to prepare the firm for worst-case scenarios with regard to both (1) the firm's intrinsic sensitivity to risk and (2) the heaviness of the severity's tail.

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