Continuous-time mean-variance asset-liability management with endogenous liabilities

Yao, Haixiang, Lai, Yongzeng and Li, Yong (2013) Continuous-time mean-variance asset-liability management with endogenous liabilities. Insurance: Mathematics and Economics, 52 1: 6-17. doi:10.1016/j.insmatheco.2012.10.001

Author Yao, Haixiang
Lai, Yongzeng
Li, Yong
Title Continuous-time mean-variance asset-liability management with endogenous liabilities
Journal name Insurance: Mathematics and Economics   Check publisher's open access policy
ISSN 0167-6687
Publication date 2013-01
Sub-type Article (original research)
DOI 10.1016/j.insmatheco.2012.10.001
Volume 52
Issue 1
Start page 6
End page 17
Total pages 12
Place of publication Netherlands
Publisher Elsevier North-Holland
Collection year 2014
Language eng
Formatted abstract
This paper investigates a continuous-time mean–variance asset–liability management problem with endogenous liabilities in a more general market where all the assets can be risky. Different from exogenous liabilities that cannot be controlled, the endogenous liabilities can be controlled by various financial instruments and investors’ decisions. For example, a company can raise fund by issuing different kinds of bonds. Types and quantities of the bonds are controlled by the company itself. Investors optimize allocation not only for their assets, but also for their liabilities under our model. This makes the analysis of the problem more challenging than in the setting based on exogenous liabilities. In this paper, we first prove the existence and uniqueness of the solution to the associated Riccati-type equation by using the Khatri–Rao product technique and the relevant stochastic control theory; we then derive closed form expressions of the efficient strategy and the mean–variance efficient frontier by using the Lagrange multiplier method and the Hamilton–Jacobi–Bellman equation approach, and we next discuss two degenerated cases; finally, we present some numerical examples to illustrate the results obtained in this paper.

Highlights ► A continuous-time mean–variance model with endogenous liabilities is studied. ► The Lagrange multiplier method, the HJB approach and the Khatri–Rao product technique are used. ► The existence and uniqueness of the solution to the related Riccati equation are proved. ► Explicit expressions of the efficient strategy and frontier are derived. ► Two degenerate cases are discussed and some numerical examples are presented.
Keyword Endogenous liabilities
Asset-liability management
Efficient frontier
Hamilton-Jacobi-Bellman equation
Linear-quadratic regulators
Control weight costs
Portfolio selection
Stochastic control
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: Official 2014 Collection
UQ Business School Publications
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Citation counts: TR Web of Science Citation Count  Cited 10 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 15 times in Scopus Article | Citations
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