Faculty of Economics and Business Administration Publications Database

A Dynamic Programming Approach to Constrained Portfolios

Steffensen, Mogens
Volume: 229
Number: 2
Pages: 453 - 461
Month: September
ISSN-Print: 0377-2217
Link External Source: Online Version
Year: 2013
Keywords: Finance; Markov processes; Consumption investment problems; Utility maximization; Bellman equations
Abstract: This paper studies constrained portfolio problems that may involve constraints on the probability or the expected size of a shortfall of wealth or consumption. Our first contribution is that we solve the problems by dynamic programming, which is in contrast to the existing literature that applies the martingale method. More precisely, we construct the non-separable value function by formalizing the optimal constrained terminal wealth to be a (conjectured) contingent claim on the optimal non-constrained terminal wealth. This is relevant by itself, but also opens up the opportunity to derive new solutions to constrained problems. As a second contribution, we thus derive new results for non-strict constraints on the shortfall of intermediate wealth and/or consumption.