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Optimal Design of Dynamic Default Risk Measures

Part of:Probabilistic methods, simulation and stochastic differential equationsStochastic analysisStochastic processes

Published online by Cambridge University Press:  30 January 2018

Leo Shen and
Robert Elliott
Leo Shen*
Affiliation:
University of Adelaide
Robert Elliott*
Affiliation:
University of Adelaide
*
∗ Current address: WH Bryan Mining and Geology Research Centre, Sustainable Minerals Institute, The University of Queensland, Brisbane, QLD 4072, Australia. Email address: b.shen1@uq.edu.au
∗∗ Postal address: School of Mathematical Sciences, North Terrace Campus, University of Adelaide, SA 5005, Australia. Email address: robert.elliott@adelaide.edu.au
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Abstract

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We consider the question of an optimal transaction between two investors to minimize their risks. We define a dynamic entropic risk measure using backward stochastic differential equations related to a continuous-time single jump process. The inf-convolution of dynamic entropic risk measures is a key transformation in solving the optimization problem.

Keywords

Inf-convolutiondynamic entropic risk measuresingle jump processbackward stochastic differential equation

MSC classification

Primary:60H10: Stochastic ordinary differential equations
Secondary:60G42: Martingales with discrete parameter65C30: Stochastic differential and integral equations

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 4 , December 2012, pp. 967 - 977
Copyright
© Applied Probability Trust 

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