A Dynamic Programming Approach to Constrained Portfolios

TY - JOUR

T1 - A Dynamic Programming Approach to Constrained Portfolios

AU - Kraft, Holger

AU - Steffensen, Mogens

PY - 2013/9/1

Y1 - 2013/9/1

N2 - 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.

AB - 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.

U2 - 10.1016/j.ejor.2013.02.039

DO - 10.1016/j.ejor.2013.02.039

M3 - Journal article

SN - 0377-2217

VL - 229

SP - 453

EP - 461

JO - European Journal of Operational Research

JF - European Journal of Operational Research

IS - 2

ER -