Quadratic Unconstrained Binary Optimization Approach for Incorporating Solvency Capital into Portfolio Optimization
Abstract
:1. Introduction
1.1. Our Contribution
1.2. Multi-Objective Portfolio Optimization
1.3. Extension of Portfolio Optimization by Solvency Capital Requirement
1.4. Finding Pareto-Optimal Points by Solving QUBOs
2. The QUBO Formulation
2.1. Finding a Quadratic Approximation for SCR
2.2. Discretization of Continuous Variables
2.3. Constraints
3. Experimental Results
3.1. Results on the Quadratic Approximation of SCR
3.2. Results on Solving the Multi-Objective Problem
4. Conclusions and Future Research
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
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Asset Class i | Asset Class i | ||||
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1 | 14 | ||||
2 | 15 | ||||
3 | 16 | ||||
4 | 17 | ||||
5 | 18 | ||||
6 | 19 | ||||
7 | 20 | ||||
8 | 21 | ||||
9 | 22 | ||||
10 | 23 | ||||
11 | 24 | ||||
12 | 25 | ||||
13 | 26 |
Epoch | 1 | 2 | 10 | 100 |
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Training Error | ||||
Validation Error |
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Turkalj, I.; Assadsolimani, M.; Braun, M.; Halffmann, P.; Hegemann, N.; Kerstan, S.; Maciejewski, J.; Sharma, S.; Zhou, Y. Quadratic Unconstrained Binary Optimization Approach for Incorporating Solvency Capital into Portfolio Optimization. Risks 2024, 12, 23. https://doi.org/10.3390/risks12020023
Turkalj I, Assadsolimani M, Braun M, Halffmann P, Hegemann N, Kerstan S, Maciejewski J, Sharma S, Zhou Y. Quadratic Unconstrained Binary Optimization Approach for Incorporating Solvency Capital into Portfolio Optimization. Risks. 2024; 12(2):23. https://doi.org/10.3390/risks12020023
Chicago/Turabian StyleTurkalj, Ivica, Mohammad Assadsolimani, Markus Braun, Pascal Halffmann, Niklas Hegemann, Sven Kerstan, Janik Maciejewski, Shivam Sharma, and Yuanheng Zhou. 2024. "Quadratic Unconstrained Binary Optimization Approach for Incorporating Solvency Capital into Portfolio Optimization" Risks 12, no. 2: 23. https://doi.org/10.3390/risks12020023