Validity of portfolio bounds from sub- and supersolutions

Determine whether the sub- and supersolution-based approximations in the numerical illustration of the Volterra Heston model yield, respectively, upper and lower bounds on the optimal portfolio allocation.

Background

The paper constructs sub- and supersolutions for the integrated-variance-clock BSDE and uses them to approximate optimal consumption and portfolio strategies in the incomplete Volterra Heston model. The sub- and supersolutions provide bounds for the optimal consumption rate, but the relationship between their associated portfolio controls and the true optimal portfolio is not established.

Consequently, the numerical portfolio curves are presented as approximations rather than rigorously certified bounds. Resolving whether the sub- and supersolution portfolios bound the optimal portfolio would clarify the reliability and interpretation of the numerical method.