Symmetrical solutionsof backward stochastic Volterra integral equations and theirapplications

Tianxiao Wang; Yufeng Shi

doi:10.3934/dcdsb.2010.14.251

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2010, Volume 14, Issue 1: 251-274. Doi: 10.3934/dcdsb.2010.14.251

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Symmetrical solutions of backward stochastic Volterra integral equations and their applications

Tianxiao Wang^1, and
Yufeng Shi^2,

1.
Institute for Financial Studies and School of Mathematics, Shandong University, Jinan 250100
2.
School of Mathematics, Shandong University, Jinan 250100

Received: August 31, 2009

Revised: February 28, 2010

Published: June 2010

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Abstract

Backward stochastic Volterra integral equations (BSVIEs in short) are studied. We introduce the notion of adapted symmetrical solutions (S-solutions in short), which are different from the M-solutions introduced by Yong [16]. We also give some new results for them. At last a class of dynamic coherent risk measures were derived via certain BSVIEs.

Keywords:

Backward stochastic Volterra integral equations,
Adapted symmetrical solutions,
Dynamic coherent risk measure.

Mathematics Subject Classification: 60H20, 60H07, 91B30, 91B70.

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