Some Solvable Portfolio Problems with Quadratic and Collective Objectives

Abstract

We present a verification result for a general class of portfolio problems, where the standard dynamic programming principle does not hold. Explicit solutions to a series of cases are provided. They include dynamic mean-standard deviation, endogenous habit formation for quadratic utility, and group utility. The latter is defined by adding up the certainty equivalents of the group members, and the problem is solved for exponential and power utility.