Optimal lifetime consumption-portfolio strategies under trading constraints and generalized recursive preferences.
type: Item
instance of: scholarly article
title: Optimal lifetime consumption-portfolio strategies under trading constraints and generalized recursive preferences.
zbMATH Open document ID: 1075.91026
author: Mark Schroder
author: Costis Skiadas
published in: Stochastic Processes and their Applications
publication date: 2005-11-29T00:00:00Z
review text: The paper extends the earlier results of the same authors, concerning optimal consumption and security trading strategies of an agent with non-additive preferences, to the case of general-form convex position restrictions (including market incompleteness as a special case). To formally restate the agent's optimization problem for the trading constraint case in terms similar to the ones of the unconstrained portfolio choice problem, one needs to redefine the short risk-free interest rate process and the vector of risk prices. The most general results of the paper for the diffusion price uncertainty set-up are stated with the help of the utility gradient approach. The authors provide a characterization of the utility gradient density process. The first-order optimality conditions are obtained as a system of constrained forward-backward stochastic differential equations (FBSDE). These conditions are then simplified for homothetic recursive utilities (meaning degree-one homogeneity of the aggregator function). Then, instead of the original FBSDE system, the first-order conditions reduce to a constrained backward SDE for the Lagrange multiplier of wealth. The optimal consumption process can be characterized by an explicit SDE as well.
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 49L20
zbMATH DE Number: 2233800
zbMATH Keywords: recursive utility
zbMATH Keywords: optimal consumption
zbMATH Keywords: trading constraints
zbMATH Keywords: backward stochastic differential equation
reviewed by: Alexis Derviz
MaRDI profile type: Publication
full work available at URL: j.spa.2003.09.001
OpenAlex ID: W3124163886
cites work: Ambiguity, Risk, and Asset Returns in Continuous Time
cites work: Optimal consumption and portfolio policies when asset prices follow a diffusion process
cites work: Convex duality in constrained portfolio optimization
cites work: Q4794153
cites work: Stochastic Differential Utility
cites work: Continuous-time security pricing. A utility gradient approach
cites work: A term structure model with preferences for the timing of resolution of uncertainty
cites work: Affine processes and applications in finance
cites work: A dynamic maximum principle for the optimization of recursive utilities under constraints.
cites work: Risk, ambiguity and the Savage axioms
cites work: Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework
cites work: Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case
cites work: A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
cites work: Optimal Portfolio and Consumption Decisions for a “Small Investor” on a Finite Horizon
cites work: Martingale and Duality Methods for Utility Maximization in an Incomplete Market
cites work: Q3220809
cites work: A Smooth Model of Decision Making under Ambiguity
cites work: Backward stochastic differential equations and partial differential equations with quadratic growth.
cites work: A Generalized Stochastic Differential Utility
cites work: Backward stochastic differential equations with continuous coefficient
cites work: On the existence or non-existence of solutions for certain backward stochastic differential equations
cites work: Solving forward-backward stochastic differential equations explicitly -- a four step scheme
cites work: Optimum consumption and portfolio rules in a continuous-time model
cites work: Adapted solution of a backward stochastic differential equation
cites work: Optimal consumption and portfolio selection with stochastic differential utility
cites work: Lifetime consumption-portfolio choice under trading constraints, recursive preferences, and nontradeable income
cites work: OPTIMALITY AND STATE PRICING IN CONSTRAINED FINANCIAL MARKETS WITH RECURSIVE UTILITY UNDER CONTINUOUS AND DISCONTINUOUS INFORMATION
cites work: First order versus second order risk aversion
cites work: A duality method for optimal consumption and investment under short- selling prohibition. I: General market coefficients
cites work: Recursive utility and preferences for information
cites work: Robust control and recursive utility
cites work: Portfolio choice with non-expected utility in continuous time
cites work: Q4255599
DOI: 10.1016/J.SPA.2003.09.001
description: scientific article