Optimal Portfolio and Consumption Decisions for a “Small Investor” on a Finite Horizon

Abstract

Abstract. A general consumption/investment problem is considered for an agent whose actions cannot affect the market prices, and who strives to maximize total expected discounted utility of both consumption and terminal wealth. Under very general conditions on the nature of the market model and on the utility functions of the agent, it is shown how to approach the above problem by considering separately the two more elementary ones of maximizing utility of consumption only and of maximizing utility of terminal wealth only, and then appropriately composing them. The optimal consumption and wealth processes are obtained quite explicitly. In the case of a market model with constant coefficients,, the optimal portfolio and consumption rules are derived very explicitly in feedback form (on the current level of wealth).

Optimal Consumption and Portfolio Selection with Stochastic Differential Utility

“…This effect is also related to attitudes toward the timing of resolution of uncertainty, as discussed, among others, by Kreps and Porteus [35], Chew and Epstein [3,4], and Skiadas [47], the last reference covering the case of SDU. The paper's approach generalizes the Karatzas et al [31], and Cox and Huang [5,6] treatments 2 of Merton's [40] optimal portfolio selection problem with additive utilities (textbook accounts of which are given by Merton [41], Duffie [11], and Karatzas and Shreve [33]). The basic idea is to utilize market completeness to separate the computation of an optimal consumption plan and that of a corresponding trading strategy.…”

Optimal lifetime consumption and investment under a drawdown constraint

“…One also easily checks thatX * t 13) so that the unique solution of (2.9) is obtained by combining (2.10), (2.12) and (2.13):…”

“…The case of incomplete markets was first considered by Cox and Huang [4] and Karatzas, Lehoczky and Shreve [13]. Cvitanić and Karatzas [5] considered the case where the agent portfolio is restricted to take values in some given closed convex set.…”

Asset and commodity prices with multi-attribute durable goods

“…By definition these processes are T - The static optimization problem associated with the dynamic optimization problem of the agent is Huang (1989, 1991), Karatzas, Lehoczky and Shreve (1987)),…”