Optimal Consumption and Portfolio Decision with Heston’s SV Model Under HARA Utility Criterion

Wang Chunfeng (), Chang Hao () and Fang Zhenming ()
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Wang Chunfeng: College of Management and Economics, Tianjin University, Tianjin300072, China
Chang Hao: College of Management and Economics, Tianjin University, Tianjin300072, China
Fang Zhenming: College of Management and Economics, Tianjin University, Tianjin300072, China

Journal of Systems Science and Information, 2017, vol. 5, issue 1, 21-33

Abstract: This paper studies the optimal consumption-investment strategy with Heston’s stochastic volatility (SV) model under hyperbolic absolute risk aversion (HARA) utility criterion. The financial market is composed of a risk-less asset and a risky asset, whose price process is supposed to be driven by Heston’s SV model. The risky preference of the individual is assumed to satisfy HARA utility, which recovers power utility, exponential utility and logarithm utility as special cases. HARA utility is of general framework in the utility theory and is seldom studied in the existing literatures. Legendre transform-dual technique along with stochastic dynamic programming principle is presented to deal with our problem and the closed-form solution to the optimal consumption-investment strategy is successfully obtained. Finally, some special cases are derived in detail.

Keywords: investment-consumption problem; Heston model; HARA preference; Legendre transformdual theory; closed-form solution (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:jossai:v:5:y:2017:i:1:p:21-33:n:2

DOI: 10.21078/JSSI-2017-021-13

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