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Asset-liability management under benchmark and mean-variance criteria in a jump diffusion market

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Abstract

This paper investigates continuous-time asset-liability management under benchmark and mean-variance criteria in a jump diffusion market. Specifically, the authors consider one risk-free asset, one risky asset and one liability, where the risky asset’s price is governed by an exponential Lévy process, the liability evolves according to a Lévy process, and there exists a correlation between the risky asset and the liability. Two models are established. One is the benchmark model and the other is the mean-variance model. The benchmark model is solved by employing the stochastic dynamic programming and its results are extended to the mean-variance model by adopting the duality theory. Closed-form solutions of the two models are derived.

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Correspondence to Zhongfei Li.

Additional information

This research is supported by the National Science Foundation for Distinguished Young Scholars under Grant No. 70825002, the National Natural Science Foundation of China under Grant No. 70518001, and the National Basic Research Program of China 973 Program under Grant No. 2007CB814902.

This paper was recommended for publication by Editor Shouyang WANG

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Zeng, Y., Li, Z. Asset-liability management under benchmark and mean-variance criteria in a jump diffusion market. J Syst Sci Complex 24, 317–327 (2011). https://doi.org/10.1007/s11424-011-9105-1

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  • DOI: https://doi.org/10.1007/s11424-011-9105-1

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