Emre Kaplaner: Dynamic Mean–Variance Portfolio Choice: Markowitz Foundations, Time Inconsistency, and Game-Theoretic Equilibria

Abstract

This thesis investigates dynamic mean–variance portfolio optimization with a focus on the fundamental challenge of time inconsistency. In the classical single-period setting, one obtains a clear risk–return trade-off via a quadratic optimization, but extending to multiperiod or continuous-time horizons reveals that variance penalties cannot be nested in the usual recursive optimization framework. To overcome this, we adopt a game-theoretic intrapersonal approach in which each date-t decision-maker is treated as a “player” sharing the same preferences but controlling only that period’s choice. A time-consistent policy is then defined as a subgame-perfect equilibrium: no future self can profitably deviate when all others stick to the prescribed strategy. We derive the corresponding extended Bellman recursions in discrete time and outline the continuous-time analogue as an equilibrium HJB system. By solving these equations in representative examples, we demonstrate a tractable method for generating dynamically credible mean–variance strategies that respect real-world constraints.