scholarly journals Two-Stage Robust Optimization Model for Uncertainty Investment Portfolio Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Dongqing Luan ◽  
Chuming Wang ◽  
Zhong Wu ◽  
Zhijie Xia
Keyword(s):  
Robust Optimization ◽  
Financial Management ◽  
Value At Risk ◽  
Optimization Theory ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Equal Weight ◽  
Investment Portfolio ◽  
Two Stage ◽  
Mip Model

Investment portfolio can provide investors with a more robust financial management plan, but the uncertainty of its parameters is a key factor affecting performance. This paper conducts research on investment portfolios and constructs a two-stage mixed integer programming (TS-MIP) model, which comprehensively considers the five dimensions of profit, diversity, skewness, information entropy, and conditional value at risk. But the deterministic TS-MIP model cannot cope with the uncertainty. Therefore, this paper constructs a two-stage robust optimization (TS-RO) model by introducing robust optimization theory. In case experiments, data crawler technology is used to obtain actual data from real websites, and a variety of methods are used to verify the effectiveness of the proposed model in dealing with uncertainty. The comparison of models found that, compared with the traditional equal weight model, the investment benefits of the TS-MIP model and the TS-RO model proposed have been improved. Among them, the Sharpe ratio, Sortino ratio, and Treynor ratio have the largest increase of 19.30%, 8.25%, and 7.34%, respectively.

scholarly journals Convex approximations for two-stage mixed-integer mean-risk recourse models with conditional value-at-risk

2019 ◽  
Vol 181 (2) ◽  
pp. 473-507 ◽  
Author(s):  
E. Ruben van Beesten ◽  
Ward Romeijnders
Keyword(s):  
At Risk ◽  
Error Bounds ◽  
Value At Risk ◽  
Risk Measure ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Two Stage ◽  
Special Cases ◽  
Integer Recourse ◽  
Mean Risk

Abstract In traditional two-stage mixed-integer recourse models, the expected value of the total costs is minimized. In order to address risk-averse attitudes of decision makers, we consider a weighted mean-risk objective instead. Conditional value-at-risk is used as our risk measure. Integrality conditions on decision variables make the model non-convex and hence, hard to solve. To tackle this problem, we derive convex approximation models and corresponding error bounds, that depend on the total variations of the density functions of the random right-hand side variables in the model. We show that the error bounds converge to zero if these total variations go to zero. In addition, for the special cases of totally unimodular and simple integer recourse models we derive sharper error bounds.

scholarly journals Optimal Coordinated Bidding of a Profit Maximizing, Risk-Averse EV Aggregator in Three-Settlement Markets Under Uncertainty

Energies ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1755 ◽  
Author(s):  
Yelena Vardanyan ◽  
Henrik Madsen
Keyword(s):  
Real Time ◽  
Value At Risk ◽  
Risk Measure ◽  
Convex Combination ◽  
Computation Time ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Two Stage ◽  
Mixed Integer Linear Program ◽  
Market Prices

This paper develops a two-stage stochastic and dynamically updated multi-period mixed integer linear program (SD-MILP) for optimal coordinated bidding of an electric vehicle (EV) aggregator to maximize its profit from participating in competitive day-ahead, intra-day and real-time markets. The hourly conditional value at risk (T-CVaR) is applied to model the risk of trading in different markets. The objective of two-stage SD-MILP is modeled as a convex combination of the expected profit and the T-CVaR hourly risk measure. When day-ahead, intra-day and real-time market prices and fleet mobility are uncertain, the proposed two-stage SD-MILP model yields optimal EV charging/discharging plans for day-ahead, intra-day and real-time markets at per device level. The degradation costs of EV batteries are precisely modeled. To reflect the continuous clearing nature of the intra-day and real-time markets, rolling planning is applied, which allows re-forecasting and re-dispatching. The proposed two-stage SD-MILP is used to derive a bidding curve of an aggregator managing 1000 EVs. Furthermore, the model statistics and computation time are recorded while simulating the developed algorithm with 5000 EVs.

scholarly journals Risk-Averse Multi-Stage Stochastic Programming to Optimizing Vaccine Allocation and Treatment Logistics for Effective Epidemic Response

2021 ◽  
Author(s):  
Xuecheng Yin ◽  
Esra Buyuktahtakin
Keyword(s):  
Value At Risk ◽  
Virus Disease ◽  
Risk Measure ◽  
Adverse Outcomes ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Expected Number ◽  
Multi Stage ◽  
Stochastic Mixed Integer Programming

Existing compartmental-logistics models in epidemics control are limited in terms of optimizing the allocation of vaccines and treatment resources under a risk-averse objective. In this paper, we present a data-driven, mean-risk, multi-stage, stochastic epidemics-vaccination-logistics model that evaluates various disease growth scenarios under the Conditional Value-at-Risk (CVaR) risk measure to optimize the distribution of treatment centers, resources, and vaccines, while minimizing the total expected number of infections, deaths, and close contacts of infected people under a limited budget. We integrate a new ring vaccination compartment into a Susceptible-Infected-Treated-Recovered-Funeral-Burial epidemics-logistics model. Our formulation involves uncertainty both in the vaccine supply and the disease transmission rate. Here, we also consider the risk of experiencing scenarios that lead to adverse outcomes in terms of the number of infected and dead people due to the epidemic. Combining the risk-neutral objective with a risk measure allows for a trade-off between the weighted expected impact of the outbreak and the expected risks associated with experiencing extremely disastrous scenarios. We incorporate human mobility into the model and develop a new method to estimate the migration rate between each region when data on migration rates is not available. We apply our multi-stage stochastic mixed-integer programming model to the case of controlling the 2018-2020 Ebola Virus Disease (EVD) in the Democratic Republic of the Congo (DRC) using real data. Our results show that increasing the risk-aversion by emphasizing potentially disastrous outbreak scenarios reduces the expected risk related to adverse scenarios at the price of the increased expected number of infections and deaths over all possible scenarios. We also find that isolating and treating infected individuals are the most efficient ways to slow the transmission of the disease, while vaccination is supplementary to primary interventions on reducing the number of infections. Furthermore, our analysis indicates that vaccine acceptance rates affect the optimal vaccine allocation only at the initial stages of the vaccine rollout under a tight vaccine supply.

scholarly journals A Data-Driven Scheduling Approach for Hydrogen Penetrated Energy System Using LSTM Network

2019 ◽  
Vol 11 (23) ◽  
pp. 6784
Author(s):  
Suyang Zhou ◽  
Di He ◽  
Zhiyang Zhang ◽  
Zhi Wu ◽  
Wei Gu ◽  
...  
Keyword(s):  
Value At Risk ◽  
High Speed ◽  
Energy System ◽  
Data Driven ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Data Driven Approach ◽  
Lstm Network ◽  
Rolling Optimization ◽  
Optimization Mechanism

Intra-day control and scheduling of energy systems require high-speed computation and strong robustness. Conventional mathematical driven approaches usually require high computation resources and have difficulty handling system uncertainties. This paper proposes two data-driven scheduling approaches for hydrogen penetrated energy system (HPES) operational scheduling. The two data-driven approaches learn the historical optimization results calculated out using the mixed integer linear programing (MILP) and conditional value at risk (CVaR), respectively. The intra-day rolling optimization mechanism is introduced to evaluate the proposed data-driven scheduling approaches, MILP data-driven approach and CVaR data-driven approach, along with the forecasted renewable generation and load demands. Results show that the two data-driven approaches have lower intra-day operational costs compared with the MILP based method by 1.17% and 0.93%. In addition, the combined cooling and heating plant (CCHP) has a lower frequency of changing the operational states and power output when using the MILP data-driven approach compared with the mathematical driven approaches.

scholarly journals Robust Optimization-Based Commodity Portfolio Performance

2020 ◽  
Vol 8 (3) ◽  
pp. 54
Author(s):  
Ramesh Adhikari ◽  
Kyle J. Putnam ◽  
Humnath Panta
Keyword(s):  
At Risk ◽  
Robust Optimization ◽  
Value At Risk ◽  
Optimization Technique ◽  
Practical Importance ◽  
Optimization Techniques ◽  
Commodity Futures ◽  
Conditional Value At Risk ◽  
Holding Period ◽  
Mean Variance

This paper examines the performance of a naïve equally weighted buy-and-hold portfolio and optimization-based commodity futures portfolios for various lookback and holding periods using data from January 1986 to December 2018. The application of Monte Carlo simulation-based mean-variance and conditional value-at-risk optimization techniques are used to construct the robust commodity futures portfolios. This paper documents the benefits of applying a sophisticated, robust optimization technique to construct commodity futures portfolios. We find that a 12-month lookback period contains the most useful information in constructing optimization-based portfolios, and a 1-month holding period yields the highest returns among all the holding periods examined in the paper. We also find that an optimized conditional value-at-risk portfolio using a 12-month lookback period outperforms an optimized mean-variance portfolio using the same lookback period. Our findings highlight the advantages of using robust optimization for portfolio formation in the presence of return uncertainty in the commodity futures markets. The results also highlight the practical importance of choosing the appropriate lookback and holding period when using robust optimization in the commodity portfolio formation process.

scholarly journals Dynamic economic dispatch of wind-storage combined system based on conditional value-at-risk

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Yi Zheng ◽  
Xiaoqing Bai
Keyword(s):  
At Risk ◽  
Energy Storage ◽  
Value At Risk ◽  
Economic Dispatch ◽  
Second Order ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Combined System ◽  
Dynamic Economic Dispatch ◽  
Bus System

AbstractWind power's uncertainty is from the intermittency and fluctuation of wind speed, which brings a great challenge to solving the power system's dynamic economic dispatch problem. With the wind-storage combined system, this paper proposes a dynamic economic dispatch model considering AC optimal power flow based on Conditional Value-at-Risk ($$CVaR$$ CVaR ). Since the proposed model is hard to solve, we use the big-M method and second-order cone description technique to transform it into a trackable mixed-integer second-order conic programming (MISOCP) model. By comparing the dispatching cost of the IEEE 30-bus system and the IEEE 118-bus system at different confidence levels, it is indicated that $$CVaR$$ CVaR method can adequately estimate dispatching risk and assist decision-makers in making reasonable dispatching schedules according to their risk tolerance. Meanwhile, the optimal operational energy storage capacity and initial/final energy storage state can be determined by analyzing the dispatching cost risk under different storage capacities and initial/final states.

scholarly journals A Two-Stage Optimal Dispatching Model for Micro Energy Grid Considering the Dual Goals of Economy and Environmental Protection under CVaR

2021 ◽  
Vol 13 (18) ◽  
pp. 10173
Author(s):  
Jun Dong ◽  
Yaoyu Zhang ◽  
Yuanyuan Wang ◽  
Yao Liu
Keyword(s):  
Renewable Energy ◽  
Environmental Protection ◽  
Value At Risk ◽  
Operating Cost ◽  
Optimal Scheduling ◽  
Pollutant Emission ◽  
Conditional Value At Risk ◽  
Two Stage ◽  
Environmental Objectives ◽  
Energy Grid

With the development of distributed renewable energy, a micro-energy grid (MEG) is an important way to solve the problem of energy supply in the future. A two-stage optimal scheduling model considering economy and environmental protection is proposed to solve the problem of optimal scheduling of micro-energy grid with high proportion of renewable energy system (RES) and multiple energy storage systems (ESS), in which the risk is measured by conditional value-at-risk (CVaR). The results show that (a) this model can realize the optimal power of various energy equipment, promote the consumption of renewable energy, and the optimal operating cost of the system is 34873 USD. (b) The dispatch of generating units is different under different risk coefficients λ, which leads to different dispatch cost and risk cost, and the two costs cannot be optimal at the same time. The risk coefficient λ shall be determined according to the degree of risk preference of the decision-maker. (c) The proposed optimal model could balance economic objectives and environmental objectives, and rationally control its pollutant emission level while pursuing the minimum operation costs. Therefore, the proposed model can not only reduce the operation cost based on the consideration of system carbon emissions but also provide decision-makers with decision-making support by measuring the risk.

scholarly journals Exploiting the Structure of Two-Stage Robust Optimization Models with Exponential Scenarios

2020 ◽  
Author(s):  
Hossein Hashemi Doulabi ◽  
Patrick Jaillet ◽  
Gilles Pesant ◽  
Louis-Martin Rousseau
Keyword(s):  
Robust Optimization ◽  
Single Stage ◽  
Mixed Integer ◽  
Optimization Models ◽  
Master Problem ◽  
Maximization Problem ◽  
Planning Problem ◽  
Two Stage ◽  
Integer Programs ◽  
Mixed Integer Programs

This paper addresses a class of two-stage robust optimization models with an exponential number of scenarios given implicitly. We apply Dantzig–Wolfe decomposition to exploit the structure of these models and show that the original problem reduces to a single-stage robust problem. We propose a Benders algorithm for the reformulated single-stage problem. We also develop a heuristic algorithm that dualizes the linear programming relaxation of the inner maximization problem in the reformulated model and iteratively generates cuts to shape the convex hull of the uncertainty set. We combine this heuristic with the Benders algorithm to create a more effective hybrid Benders algorithm. Because the master problem and subproblem in the Benders algorithm are mixed-integer programs, it is computationally demanding to solve them optimally at each iteration of the algorithm. Therefore, we develop novel stopping conditions for these mixed-integer programs and provide the relevant convergence proofs. Extensive computational experiments on a nurse planning problem and a two-echelon supply chain problem are performed to evaluate the efficiency of the proposed algorithms.

scholarly journals K-adaptability in two-stage mixed-integer robust optimization

2019 ◽  
Vol 12 (2) ◽  
pp. 193-224 ◽  
Author(s):  
Anirudh Subramanyam ◽  
Chrysanthos E. Gounaris ◽  
Wolfram Wiesemann
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Mixed Integer ◽  
Finite Convergence ◽  
Two Stage ◽  
Infinite Dimensional ◽  
Benchmark Data ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation

Abstract We study two-stage robust optimization problems with mixed discrete-continuous decisions in both stages. Despite their broad range of applications, these problems pose two fundamental challenges: (i) they constitute infinite-dimensional problems that require a finite-dimensional approximation, and (ii) the presence of discrete recourse decisions typically prohibits duality-based solution schemes. We address the first challenge by studying a K-adaptability formulation that selects K candidate recourse policies before observing the realization of the uncertain parameters and that implements the best of these policies after the realization is known. We address the second challenge through a branch-and-bound scheme that enjoys asymptotic convergence in general and finite convergence under specific conditions. We illustrate the performance of our algorithm in numerical experiments involving benchmark data from several application domains.

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