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A bi-level optimization model for the asset-liability management of insurance companies

  • *Corresponding author: Xiaowei Chen

    *Corresponding author: Xiaowei Chen 

The first author is supported by National Natural Science Foundation of China No. 61673225

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  • Different from traditional asset-liability management where only investment allocation is considered, this paper introduces policy product allocation into asset-liability management of insurance companies. In order to balance product allocation and investment allocation, a bi-level optimization model is employed. Since the decision-making environment of the two allocation processes is full of indeterminacy, the imprecise information of the model is measured by uncertain variables in order to deal with the lack of enough historical data. To solve this bi-level Optimization problem containing uncertain variables, an uncertain bilevel programming model is used. Furthermore, we simulate a scenario to compare the bi-level optimization approach with other approaches by virtue of hybrid intelligent algorithms.

    Mathematics Subject Classification: Primary: 90B50, 91B30; Secondary: 90C70.

    Citation:

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  • Figure 1.  Stackelberg Competition

    Table 1.  Investment Items Parameters

    Investment Items $i$ Decision Variables Yield rate $\xi_{i}$ Beta-Value $\beta_{i}$ Unsystematic risk $\sigma_{i}$
    Risk asset 1 $1$ $A_{1}$ ${\mathcal{N}}(0.1,0.01)$ $0.9$ $0.01$
    Risk asset 2 $2$ $A_{2}$ ${\mathcal{N}}(0.08,0.005)$ $0.6$ $ 0.005$
    Risk-free asset $3$ $A_{3}$ $0.05$ $0.5$ $0$
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    Table 2.  Policy Products Parameters

    Policy Products $j$ Decision Variables Profit Margin $r_{j}$ drawing coefficient $\theta_{j}$ sale coefficient $s_{j}$
    Policy 1 $1$ $P_{1}$ ${\mathcal{L}}(0.1,0.12 )$ $30\%$ $1$
    Policy 2 $2$ $P_{2}$ ${\mathcal{L}}(0.08,0.11)$ $40\%$ $1.1$
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    Table 3.  Optimal Solutions of Different Programmings6

    Approaches Programmings Gross Profit Policy Allocation $\bf{P}$ Investment Allocation $\bf{A}$
    Stackelberg Competition (11) $137.2$ $(0, 1100)$ $(162, 0,277.3)$
    Decentralized Decision Making (12), (13) $135$ $(1000, 0)$ $(50,250, 0)$
    Centralized Decision Making7 (14) $134.8$ $(0, 1100)$ $(165, 0,275)$
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