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**Financial networks with intermediation: risk management with variable weights.**
*(English)*
Zbl 1107.91305

Summary: We develop a framework for the modeling, analysis, and computation of solutions to multitiered financial network problems with intermediaries in which both the sources of financial funds as well as the intermediaries are multicriteria decision-makers. In particular, we assume that these decision-makers seek not only to maximize their net revenues but also to minimize risk with the risk being penalized by a variable weight. We make explicit the behavior of the various decision-makers, including the consumers at the demand markets for the financial products. We derive the optimality conditions, and demonstrate that the governing equilibrium conditions of the financial network economy can be formulated as a finite-dimensional variational inequality problem. Qualitative properties of the equilibrium financial flow and price pattern are provided. A computational procedure that exploits the network structure of the problem is proposed and then applied to several numerical examples.

### MSC:

91B06 | Decision theory |

91B30 | Risk theory, insurance (MSC2010) |

### Keywords:

finance; networks; risk management; financial intermediation; multicriteria decision-making; equilibrium; variational inequalities
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\textit{A. Nagurney} and \textit{K. Ke}, Eur. J. Oper. Res. 172, No. 1, 40--63 (2006; Zbl 1107.91305)

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