ASSET-LIABILITY MANAGEMENT UNDER BENCHMARK AND MEAN-VARIANCECRITERIA IN A JUMP DIFFUSION MARKET

Yan ZENG;Zhongfei LI

Journal of Systems Science & Complexity ›› 2011, Vol. 24 ›› Issue (2) : 317-327.

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Journal of Systems Science & Complexity ›› 2011, Vol. 24 ›› Issue (2) : 317-327. DOI: 10.1007/s11424-011-9105-1
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ASSET-LIABILITY MANAGEMENT UNDER BENCHMARK AND MEAN-VARIANCECRITERIA 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 L\'{e}vy process, the liability evolves according to a L\'{e}vy 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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Asset-liability management / benchmark and mean-variance models / duality theory / jump diffusion market / Hamilton-Jacobi-Bellman equation.

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Yan ZENG , Zhongfei LI. ASSET-LIABILITY MANAGEMENT UNDER BENCHMARK AND MEAN-VARIANCECRITERIA IN A JUMP DIFFUSION MARKET. Journal of Systems Science and Complexity, 2011, 24(2): 317-327 https://doi.org/10.1007/s11424-011-9105-1
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