Optimal investment consumption model with a higher interest rate for borrowing
type: Item
instance of: scholarly article
title: Optimal investment consumption model with a higher interest rate for borrowing
zbMATH Open document ID: 0971.91025
author: Weiyin Fei
author: Rangquan Wu
published in: Applied Mathematics. Series B (English Edition)
publication date: 2001-10-26T00:00:00Z
review text: The paper considers a consumption-investment model for a single agent. The investor consumes the wealth \(X(t)\) at a nonnegative rate \(c(t)\) and distributes it between one riskless bond with instantaneous rate of return \(r\) and the \(d\) risk stocks whose prices are driven by a Wiener process. Stock purchases may be financed by borrowing at a higher interest rate \(R\geq r\#.\) The authors include also the dividend rate even in the case when \(R>r\) and it is the characteristic feature of the paper. The usual optimization problem with two utility functions is formulated, and a family of auxiliary optimization problems is introduced. A solution of the original problem is presented via the properties of the solutions of auxiliary problems. By using duality methods, the existence of optimal portfolio consumption is proved, and the explicit solution leading to feedback formulae are derived for deterministic coefficients.
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 49N15
Mathematics Subject Classification ID: 60H30
zbMATH DE Number: 1542577
zbMATH Keywords: stochastic control
zbMATH Keywords: consumption and investment
zbMATH Keywords: convex analysis
zbMATH Keywords: martingale
zbMATH Keywords: dividend rate
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: s11766-000-0060-1
OpenAlex ID: W60152383
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: Optimal consumption and portfolio policies when asset prices follow a diffusion process
cites work: An Optimal Investment/Consumption Model with Borrowing
cites work: Convex duality in constrained portfolio optimization
cites work: Study of constrained portfolio model on optimization of utility from terminal wealth.
cites work: Q4039796
cites work: Q3348688
cites work: Q4086525
DOI: 10.1007/S11766-000-0060-1
description: scientific article; zbMATH DE number 1542577