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Robust optimal asset-liability management with penalization on ambiguity

  • * Corresponding author: Hui Mi

    * Corresponding author: Hui Mi

The research was supported by National Natural Science Foundation of China (Grant No.61304065) and the Qing Lan Project of Jiangsu Province

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  • In this paper, we study the robust optimal asset- problems for an ambiguity-averse investor, who does not have perfect information in the drift terms of the risky asset and liability processes. Two different kinds of objectives are considered: $ (i) $ Maximizing the minimal expected utility of the terminal wealth; $ (ii) $ Minimizing the maximal cumulative deviation. The ambiguity in both problems is described by a set of equivalent measures to the reference model. By the stochastic dynamic programming approach and Hamilton-Jacobi-Bellman (HJB) equation, we derive closed-form expressions for the value function and corresponding robust optimal investment strategy in each problem. Furthermore, some special cases are provided to investigate the effect of model uncertainty on the optimal investment strategy. Finally, the economic implication and parameter sensitivity are analyzed by some numerical examples. We also compare the robust optimal investment strategies in two different problems.

    Mathematics Subject Classification: Primary: 93E20; Secondary: 91B30, 91G80.


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  • Figure 1.  The influence of $ \mu $ and $ \rho $ on the robust optimal investment strategy

    Figure 2.  The influence of $ b $ and $ \beta_1 $ on the robust optimal investment strategy

    Figure 3.  The influence of $ R $ and $ y_0 $ on the robust optimal investment strategy

    Table 1.  The basic parameters

    r μ σ a b ρ t T m β1 β2 x R y0
    0.03 0.08 0.25 0.1 0.2 0.3 0 10 0.5 0.5 0.5 1 0.1 1
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