Robust Optimal Investment Strategies for Mean-Variance Asset-Liability Management Under 4/2 Stochastic Volatility Models

Yumo Zhang ()
Additional contact information
Yumo Zhang: University of Copenhagen

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 1, 1-32

Abstract: Abstract This paper considers a robust optimal investment problem for an ambiguity-averse asset-liability manager under the mean-variance criterion in the presence of stochastic volatility. The manager has access to a risk-free (bank account) and a risky asset (stock) in a financial market. Specifically, the stock price is driven by the state-of-the-art 4/2 stochastic volatility model, which recovers the Heston model and 3/2 model, as exceptional cases. By applying the stochastic dynamic programming approach and solving the corresponding Hamilton-Jacobi-Bellman-Isaacs equation, closed-form expressions for the robust optimal strategy and optimal value function are derived. Technical conditions are determined for the verification theorem and well-defined solutions. Moreover, we provide explicit results for two special cases of our model, the ambiguity-neutral manager case and the case without random liabilities. Finally, some numerical examples are presented to illustrate the effects of model parameters on the robust optimal control and optimal value function (efficient frontier). The numerical examples show that the ambiguity aversion levels about the risky asset price and its volatility have different impacts on the amount of wealth invested in the risky asset and on the efficient frontier.

Keywords: Asset-liability management; Ambiguity aversion; Mean-variance criterion; Hamilton-Jacobi-Bellman-Isaacs equation; 4/2 stochastic volatility model; 60H30; 93E20; 91G10 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s11009-023-10007-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-10007-4

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-023-10007-4

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().