Optimal consumption and portfolio decision with stochastic covariance in incomplete markets

Hang Wang and Zhijun Hu

Chaos, Solitons & Fractals, 2020, vol. 138, issue C

Abstract: This paper investigates finite and infinite horizon optimal consumption and portfolio choice problems in incomplete markets with stochastic covariance among stock returns. The stock price dynamics are assumed to follow a multivariate stochastic volatility process. The Hamilton-Jacobi-Bellman (HJB) equation is derived by using dynamic programming method and the closed-form expressions for portfolio–consumption strategies are derived in the case of logarithmic utility. In the case of infinite time horizon, we prove the existence of a classical solution and provide a verification theorem. The closed form approximate solutions to the optimal consumption and portfolio polices for a power utility investor are obtained by solving the same utility maximization problem in two fictitious complete markets. Moreover, we verify the existence and optimality of the solution of the original incomplete market and also provide the upper bound of the utility loss of approximate rules. Finally, a numerical application to an incomplete market with stochastic factors show that the utility loss of the approximation rules is small and the performance of the approximate rules is close to optimal.

Keywords: Consumption and portfolio choice; CRRA-Utility; Stochastic covariance; HJB Equation; Utility loss; Incomplete markets (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077920301776
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920301776

DOI: 10.1016/j.chaos.2020.109775

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().