Abstract
We show that scalarization techniques are very important tools in several fields of mathematics, especially in multiobjective optimization, uncertain optimization, risk theory and finance. Specifically, we consider randomness in scalar optimization problems and explore important connections between a nonlinear scalarization technique, robust optimization and coherent risk measures. Furthermore, we discuss a new model for a Private Equity Fund based on stochastic differential equations. In order to find efficient strategies for the fund manager we formulate a stochastic multiobjective optimization problem for a Private Equity Fund. Using a special case of the nonlinear scalarization technique, the ε-constraint method, we solve this stochastic multiobjective optimization problem.
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Acknowledgements
The authors would like to thank two anonymous referees of this book chapter for their valuable comments and constructive suggestions. The work of A. A. K. is supported by a grant from the Simons Foundation (#210443 to Akhtar Khan).
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Khan, A.A., Köbis, E., Tammer, C. (2015). Scalarization Methods in Multiobjective Optimization, Robustness, Risk Theory and Finance. In: Al-Shammari, M., Masri, H. (eds) Multiple Criteria Decision Making in Finance, Insurance and Investment. Multiple Criteria Decision Making. Springer, Cham. https://doi.org/10.1007/978-3-319-21158-9_6
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DOI: https://doi.org/10.1007/978-3-319-21158-9_6
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