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Extending dynamic convex risk measures from discrete time to continuous time: A convergence approach

  • Stadje, Mitja

We present an approach for the transition from convex risk measures in a certain discrete time setting to their counterparts in continuous time. The aim of this paper is to show that a large class of convex risk measures in continuous time can be obtained as limits of discrete time-consistent convex risk measures. The discrete time risk measures are constructed from properly rescaled ([`]tilted') one-period convex risk measures, using a d-dimensional random walk converging to a Brownian motion. Under suitable conditions (covering many standard one-period risk measures) we obtain convergence of the discrete risk measures to the solution of a BSDE, defining a convex risk measure in continuous time, whose driver can then be viewed as the continuous time analogue of the discrete [`]driver' characterizing the one-period risk. We derive the limiting drivers for the semi-deviation risk measure, Value at Risk, Average Value at Risk, and the Gini risk measure in closed form.

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Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 47 (2010)
Issue (Month): 3 (December)
Pages: 391-404

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Handle: RePEc:eee:insuma:v:47:y:2010:i:3:p:391-404
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

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