Continuous-Time Portfolio Selection: A Cursory Survey

Abstract

In this article we provide a short survey on continuous-time portfolio selection. We explain the pioneering contribution of Merton and the use of dynamic programming. Then, we discuss Bismut's application of the Pontryagin maximum principle to portfolio selection and the dual martingale approach. We also explain two models with potential applicability to practice: life-cycle models with explicit consideration of retirement and models with protection against decline in spending power.