Mean-variance asset–liability management with partial information and uncertain time horizon

ABSTRACT

This paper studies a mean-variance asset–liability management (ALM) problem with uncertain time horizon and partial information. The ALM can invest in an incomplete financial market consisting of one riskless asset and n risky stocks. The stocks price process is described by a multidimensional diffusion process with random coefficients. The uncontrollable liability process is modelled by a general diffusion process with hedgeable risks and unhedgeable risks. The uncertainty of the time horizon is assumed to come from randomness of financial assets and the liability and some other stochastic factors. The ALM may get only partial information about the liability. We derive efficient strategies and efficient frontiers in terms of the solutions of two BSDEs under complete and partial information. The closed-form expressions of efficient strategies and efficient frontiers are obtained under some special cases.

Keywords:

• Asset
• liability
• uncertain time horizon
• partial information
• BSDE

2010 Mathematics Subject Classifications:

• 97M30
• 91G80
• 93E20
• 60H30

Acknowledgments

The authors are very grateful to the Editor and two anonymous referees for their valuable comments and suggestions, which led to an improvement of the presentation of the work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Supported in part by the National Natural Science Foundation of China [Grant Number 11701436] and the Fundamental Research Funds for the Central Universities [Grant Numbers WUT: 2018IB019 and 2018IVB014].