Decomposition of Optimal Dynamic Portfolio Choice with Wealth-Dependent Utilities in Incomplete Markets

Chenxu Li, Olivier Scaillet and Yiwen Shen
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Chenxu Li: Peking University - Guanghua School of Management
Yiwen Shen: Columbia Business School - Decision Risk and Operations

No 20-22, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: This paper establishes a new decomposition of optimal dynamic portfolio choice under general incomplete-market diffusion models by disentangling the fundamental impacts on optimal policy from market incompleteness and flexible wealth-dependent utilities. We derive explicit dynamics of the components for the optimal policy, and obtain an equation system for solving the shadow price of market incompleteness, which is found to be dependent on both market state and wealth level. We identify a new important hedge component for non-myopic investors to hedge the uncertainty in shadow price due to variation in wealth level. As an application, we establish and compare the decompositions of optimal policy under general models with the prevalent HARA and CRRA utilities. Under nonrandom but possibly time-varying interest rate, we solve in closed-form the HARA policy as a combination of a bond holding scheme and a corresponding CRRA strategy. Finally, we develop a simulation method to implement the decomposition of optimal policy under the general incomplete market setting, whereas existing approaches remain elusive.

Keywords: optimal portfolio choice; decomposition; incomplete market; wealth-dependent utility; closed-form (search for similar items in EconPapers)
JEL-codes: C61 C63 G11 (search for similar items in EconPapers)
Pages: 65 pages
Date: 2020-04
New Economics Papers: this item is included in nep-upt
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Related works:
Working Paper: Decomposition of optimal dynamic portfolio choice with wealth-dependent utilities in incomplete markets (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp2022

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