New approach to optimal control of stochastic Volterra integral equations

ABSTRACT

We study optimal control of stochastic Volterra integral equations (SVIE) with jumps by using Hida-Malliavin calculus.

• We give conditions under which there exist 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.

KEYWORDS:

• Stochastic maximum principle
• stochastic Volterra integral equation (SVIE)
• backward stochastic Volterra integral equation (BSVIE)
• Hida-Malliavin calculus
• Volterra recursive utility
• optimal consumption from an SVIE cash flow

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was carried out with support of the Norwegian Research Council, within the research project Challenges in Stochastic Control, Information and Applications (STOCONINF), project number 250768/F20.