Duality Methods

Machine-learning a family of solutions to an optimal pension investment problem ArXiv ID: 2511.07045 “View on arXiv” Authors: John Armstrong, Cristin Buescu, James Dalby, Rohan Hobbs Abstract We use a neural network to identify the optimal solution to a family of optimal investment problems, where the parameters determining an investor’s risk and consumption preferences are given as inputs to the neural network in addition to economic variables. This is used to develop a practical tool that can be used to explore how pension outcomes vary with preference parameters. We use a Black-Scholes economic model so that we may validate the accuracy of network using a classical and provably convergent numerical method developed using the duality approach. ...

Mind the Cap! – Constrained Portfolio Optimisation in Heston’s Stochastic Volatility Model ArXiv ID: 2306.11158 “View on arXiv” Authors: Unknown Abstract We consider a portfolio optimisation problem for a utility-maximising investor who faces convex constraints on his portfolio allocation in Heston’s stochastic volatility model. We apply the duality methods developed in previous work to obtain a closed-form expression for the optimal portfolio allocation. In doing so, we observe that allocation constraints impact the optimal constrained portfolio allocation in a fundamentally different way in Heston’s stochastic volatility model than in the Black Scholes model. In particular, the optimal constrained portfolio may be different from the naive capped portfolio, which caps off the optimal unconstrained portfolio at the boundaries of the constraints. Despite this difference, we illustrate by way of a numerical analysis that in most realistic scenarios the capped portfolio leads to slim annual wealth equivalent losses compared to the optimal constrained portfolio. During a financial crisis, however, a capped solution might lead to compelling annual wealth equivalent losses. ...