# 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, HaixiangLai, YongzengLi, Yong Continuous-time mean-variance asset-liability management with endogenous liabilities Insurance: Mathematics and Economics   Check publisher's open access policy 0167-66871873-5959 2013-01 Article (original research) 10.1016/j.insmatheco.2012.10.001 52 1 6 17 12 Netherlands Elsevier North-Holland 2014 eng 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. Endogenous liabilitiesMean-varianceAsset-liability managementEfficient frontierHamilton-Jacobi-Bellman equationLinear-quadratic regulatorsControl weight costsPortfolio selectionStochastic controlKhatri-RaoOptimizationFrameworkProductsModel C1 Confirmed Code UQ

 Document type: Journal Article Article (original research) Official 2014 Collection UQ Business School Publications

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