Duality methods for stochastic optimal control problems in finance

Stochastic optimal control problems can be employed to derive and examine an agent’s optimal investment-consumption decisions. In solving these problems, the technical notion of convex duality plays an important role. Convex duality can be regarded as a mathematical tool that facilitates the retrieval of analytical expressions for the optimal solutions to portfolio-based optimization problems. Mainly on account of their corresponding ability to generate unique analytical insights, duality methods constitute a powerful instrument for institutional investors and scholars alike. In this dissertation, we concentrate on both the theoretical and applied sides of these methods, using specific frameworks suitable for the study of financial decision-making. Concretely, we rely on duality principles to develop novel techniques that broaden our understanding of the dynamics underscoring an agent’s optimal investment-consumption behavior. Moreover, we make use of dual-control machinery to analyze and improve the recovery potential of a pension fund that operates according to a defined-contribution scheme. By means of these theoretical and applied studies, this dissertation predominantly contributes to the domain of portfolio optimization.