New approach to optimal control of stochastic Volterra integral equations

2017/09/16 by Agram, Nacira, Øksendal, Bernt, Yakhlef, Samia · 2 citations
#60H05 #60H20 #60J75 #91B70 #91G80 #93E20 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1709.05463

Abstract

We study optimal control of stochastic Volterra integral equations (SVIE) with jumps by using Hida-Malliavin calculus. - We give conditions under which there exists unique solutions of such equations. - Then we prove both a sufficient maximum principle (a verification theorem) and a necessary maximum principle via Hida-Malliavin calculus. - As an application we solve a problem of optimal consumption from a cash flow modelled by an SVIE.

Cited by

• Optimal control of Volterra integral diffusions and application to contract theory
• Markov approximation for controlled Hawkes Jump-Diffusions with general kernels

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• An optimal control problem of forward-backward stochastic Volterra integral equations with state constraints