Precommitted Strategies with Initial-Time and Intermediate-Time Value-at-Risk Constraints

Chufang Wu (), Jia-Wen Gu (), Wai-Ki Ching () and Chi-Wing Wong ()
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Chufang Wu: Shenzhen Polytechnic University
Jia-Wen Gu: Southern University of Science and Technology
Wai-Ki Ching: The University of Hong Kong
Chi-Wing Wong: The University of Hong Kong

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 1, No 31, 880-919

Abstract: Abstract This paper considers the expected utility portfolio optimization problem with initial-time and intermediate-time Value-at-Risk constraints on terminal wealth. We derive the closed-form solutions which are optimal among all feasible controls at initial time, i.e., precommitted strategies. Moreover, the precommitted strategies are also optimal at the intermediate time for “bad” market states. A contingent claim on Merton’s portfolio is constructed to replicate the optimal portfolio. We find that risk management with intermediate-time risk constraints is prudent in hedging “bad” intermediate market states and performs significantly better than the one terminal-wealth risk constraint solutions under the relative loss ratio measure.

Keywords: Portfolio optimization; Expected utility maximization; Intermediate-time risk measure; Precommitted strategy; Value-at-Risk; Pro-cyclicality; Compound options.; 93C95; 91B70 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02537-9

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