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Dynamic risk measures for stochastic asset processes from ruin theory

Published online by Cambridge University Press:  19 February 2018

Yasutaka Shimizu  and
Shuji Tanaka
Yasutaka Shimizu*
Affiliation:
Department of Applied Mathematics, Waseda University
Shuji Tanaka
Affiliation:
Department of Mathematics, College of Humanities and Sciences, Nihon University
*
*Correspondence to: Yasutaka Shimizu, Department of Applied Mathematics, Waseda University, Shinjuku-ku, Tokyo 169-8555, Japan. E-mail: shimizu@waseda.jp
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Abstract

This article considers a dynamic version of risk measures for stochastic asset processes and gives a mathematical benchmark for required capital in a solvency regulation framework. Some dynamic risk measures, based on the expected discounted penalty function launched by Gerber and Shiu, are proposed to measure solvency risk from the company’s going-concern point of view. This study proposes a novel mathematical justification of a risk measure for stochastic processes as a map on a functional path space of future loss processes.

Keywords

Insolvency riskGerber–Shiu functionDynamic risk measureSolvency capital requirementAsset/liability management

JEL classification

C02: Mathematical Methods G22: Insurance • Insurance Companies • Actuarial Studies G32: Financing Policy • Financial Risk and Risk Management • Capital and Ownership Structure • Value of Firms • Goodwill

Information

Type
Paper
Information
Annals of Actuarial Science , Volume 12 , Issue 2 , September 2018 , pp. 249 - 268
Copyright
© Institute and Faculty of Actuaries 2018 

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