Multistage Robust Average Randomized Spectral Risk Optimization
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arXiv
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| Format: | Preprint |
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2024
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| author | Wu, Qiong Xu, Huifu Zheng, Harry |
| author_facet | Wu, Qiong Xu, Huifu Zheng, Harry |
| contents | In this paper, we revisit the multistage spectral risk minimization models proposed by Philpott et al.~\cite{PdF13} and Guigues and Römisch \cite{GuR12} but with some new focuses. We consider a situation where the decision maker's (DM's) risk preferences may be state-dependent or even inconsistent at some states, and consequently there is not a single deterministic spectral risk measure (SRM) which can be used to represent the DM's preferences at each stage. We adopt the recently introduced average randomized SRM (ARSRM) (in \cite{li2022randomization}) to describe the DM's overall risk preference at each stage. To solve the resulting multistage ARSRM (MARSRM) problem, we apply the well-known stochastic dual dynamic programming (SDDP) method which generates a sequence of lower and upper bounds in an iterative manner. Under some moderate conditions, we prove that the optimal solution can be found in a finite number of iterations. The MARSRM model generalizes the one-stage ARSRM and simplifies the existing multistage state-dependent preference robust model \cite{liu2021multistage}, while also encompassing the mainstream multistage risk-neutral and risk-averse optimization models \cite{GuR12,PdF13}. In the absence of complete information on the probability distribution of the DM's random preferences, we propose to use distributionally robust ARSRM (DR-ARSRM) to describe the DM's preferences at each stage. We detail computational schemes for solving both MARSRM and DR-MARSRM. Finally, we examine the performance of MARSRM and DR-MARSRM by applying them to an asset allocation problem with transaction costs and compare them with standard risk neutral and risk averse multistage linear stochastic programming (MLSP) models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00892 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multistage Robust Average Randomized Spectral Risk Optimization Wu, Qiong Xu, Huifu Zheng, Harry Optimization and Control In this paper, we revisit the multistage spectral risk minimization models proposed by Philpott et al.~\cite{PdF13} and Guigues and Römisch \cite{GuR12} but with some new focuses. We consider a situation where the decision maker's (DM's) risk preferences may be state-dependent or even inconsistent at some states, and consequently there is not a single deterministic spectral risk measure (SRM) which can be used to represent the DM's preferences at each stage. We adopt the recently introduced average randomized SRM (ARSRM) (in \cite{li2022randomization}) to describe the DM's overall risk preference at each stage. To solve the resulting multistage ARSRM (MARSRM) problem, we apply the well-known stochastic dual dynamic programming (SDDP) method which generates a sequence of lower and upper bounds in an iterative manner. Under some moderate conditions, we prove that the optimal solution can be found in a finite number of iterations. The MARSRM model generalizes the one-stage ARSRM and simplifies the existing multistage state-dependent preference robust model \cite{liu2021multistage}, while also encompassing the mainstream multistage risk-neutral and risk-averse optimization models \cite{GuR12,PdF13}. In the absence of complete information on the probability distribution of the DM's random preferences, we propose to use distributionally robust ARSRM (DR-ARSRM) to describe the DM's preferences at each stage. We detail computational schemes for solving both MARSRM and DR-MARSRM. Finally, we examine the performance of MARSRM and DR-MARSRM by applying them to an asset allocation problem with transaction costs and compare them with standard risk neutral and risk averse multistage linear stochastic programming (MLSP) models. |
| title | Multistage Robust Average Randomized Spectral Risk Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2409.00892 |