Optimal scenario-dependent multivariate shortfall risk measure and its application in risk capital allocation
Optimal scenario-dependent multivariate shortfall risk measure and its application in risk capital allocation
In this paper, we propose a novel multivariate shortfall risk measure to evaluate the systemic risk of a financial system, where the allocation weight is scenario-dependent and optimally chosen from a predetermined feasible set, and examine its properties such as (quasi-)convexity and translation invariance. To compute the proposed risk measure, we reformulate it as a two-stage stochastic program. When the underlying risk is discretely distributed, the second-stage program is a finite convex program while for the continuous case, is a semi-infinite program. To tackle the latter, we use the polynomial decision rule to approximate it and reformulate it as a tractable optimization program via the standard sums-of-squares techniques. Some convergence results are established for the approximation scheme. Moreover, we apply the proposed risk measure to the risk capital allocation problem and introduce the scenario-dependent allocation strategy. In contrast to the existing allocation methods, the new approach considers losses of all scenarios and minimizes the systemic risk. We then carry out some numerical tests on the proposed model and computational schemes for a continuous system, a discrete system, and a risk capital allocation problem in life insurance. The results show that our allocation strategy performs better than the Euler allocation rule based on the expected shortfall and the method by Armenti et al., 2018, and is robust to the (un-)systemic changes of the considered dataset. Finally, we extend our model by incorporating the cost of risk capital and investigate its impact on the optimal total amount of risk capital.
Polynomial decision rule, Risk capital allocation, Risk management, Scenario-dependent allocation strategy, Scenario-dependent multivariate shortfall
322-347
Wang, Wei
8b7c2f29-8ebf-4a6b-b7ab-a7287252886c
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Ma, Tiejun
1f591849-f17c-4209-9f42-e6587b499bae
Wang, Wei
8b7c2f29-8ebf-4a6b-b7ab-a7287252886c
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Ma, Tiejun
1f591849-f17c-4209-9f42-e6587b499bae
Wang, Wei, Xu, Huifu and Ma, Tiejun
(2022)
Optimal scenario-dependent multivariate shortfall risk measure and its application in risk capital allocation.
European Journal of Operational Research, 306 (1), .
(doi:10.1016/j.ejor.2022.08.004).
Abstract
In this paper, we propose a novel multivariate shortfall risk measure to evaluate the systemic risk of a financial system, where the allocation weight is scenario-dependent and optimally chosen from a predetermined feasible set, and examine its properties such as (quasi-)convexity and translation invariance. To compute the proposed risk measure, we reformulate it as a two-stage stochastic program. When the underlying risk is discretely distributed, the second-stage program is a finite convex program while for the continuous case, is a semi-infinite program. To tackle the latter, we use the polynomial decision rule to approximate it and reformulate it as a tractable optimization program via the standard sums-of-squares techniques. Some convergence results are established for the approximation scheme. Moreover, we apply the proposed risk measure to the risk capital allocation problem and introduce the scenario-dependent allocation strategy. In contrast to the existing allocation methods, the new approach considers losses of all scenarios and minimizes the systemic risk. We then carry out some numerical tests on the proposed model and computational schemes for a continuous system, a discrete system, and a risk capital allocation problem in life insurance. The results show that our allocation strategy performs better than the Euler allocation rule based on the expected shortfall and the method by Armenti et al., 2018, and is robust to the (un-)systemic changes of the considered dataset. Finally, we extend our model by incorporating the cost of risk capital and investigate its impact on the optimal total amount of risk capital.
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More information
Accepted/In Press date: 4 August 2022
e-pub ahead of print date: 10 August 2022
Additional Information:
Funding Information:
We would like to thank four anonymous referees for their valuable comments and suggestions which help us significantly enhance the presentation of the paper. We are also thankful to the associate editor for effective handling of the review.
Publisher Copyright:
© 2022 Elsevier B.V.
Keywords:
Polynomial decision rule, Risk capital allocation, Risk management, Scenario-dependent allocation strategy, Scenario-dependent multivariate shortfall
Identifiers
Local EPrints ID: 475679
URI: http://eprints.soton.ac.uk/id/eprint/475679
ISSN: 0377-2217
PURE UUID: 3472db3b-8b96-4532-a97e-48ef1f2776ba
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Date deposited: 24 Mar 2023 17:35
Last modified: 06 Jun 2024 01:41
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Author:
Wei Wang
Author:
Huifu Xu
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