Backward stochastic Volterra integral equations and some related problems
By Jiongmin Yong. 2006
142 citations recorded by the source corpus.
Backward stochastic Volterra integral equations (BSVIEs, for short) are introduced. The existence and uniqueness of adapted solutions are established. A duality principle between linear BSVIEs and (forward) stochastic Volterra integral equations is obtained. As applications of the duality principle, a comparison theorem is proved for the adapted solutions of BSVIEs, and a Pontryagin type maximum principle is established for an optimal control of stochastic integral equations.
Subfields: Applied Mathematics, Control and Systems Engineering, Finance
View Paper: https://www.semanticscholar.org/paper/c4275b7b849ec99e9c004f51b59290425303db3d
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In Applied Mathematics
In Control and Systems Engineering
In Finance
Citations in the corpus
- Continuous-time dynamic risk measures by backward stochastic Volterra integral equations (2007, methodology): “Next, we present a lemma whose proof can be found in [12].”
- Well-posedness and regularity of backward stochastic Volterra integral equations (2008, methodology): “4. Further, as an important application, an optimal control problem for FSVIEs, which will extend some relevant results presented in [ 33 ].”
- Time-Inconsistent Optimal Control Problems and the Equilibrium HJB Equation (2012, background): “Some relevant results concerning backward stochastic Volterra integral equations (BSVIEs, for short) can be found in [25, 26].”