Stochastic Final Pit Limits: An Efficient Frontier Analysis under Geological Uncertainty in the Open-Pit Mining Industry

In the context of planning the exploitation of an open-pit mine, the final pit limit problem consists of finding the volume to be extracted so that it maximizes the total profit of exploitation subject to overall slope angles to keep pit walls stable. To address this problem, the ore deposit is discretized as a block model, and efficient algorithms are used to find the optimal final pit. However, this methodology assumes a deterministic scenario, i.e., it does not consider that information, such as ore grades, is subject to several sources of uncertainty. This paper presents a model based on stochastic programming, seeking a balance between conflicting objectives: on the one hand, it maximizes the expected value of the open-pit mining business and simultaneously minimizes the risk of losses, measured as conditional value at risk, associated with the uncertainty in the estimation of the mineral content found in the deposit, which is characterized by a set of conditional simulations. This allows generating a set of optimal solutions in the expected return vs. risk space, forming the Pareto front or efficient frontier of final pit alternatives under geological uncertainty. In addition, some criteria are proposed that can be used by the decision maker of the mining company to choose which final pit best fits the return/risk trade off according to its objectives. This methodology was applied on a real case study, making a comparison with other proposals in the literature. The results show that our proposal better manages the relationship in controlling the risk of suffering economic losses without renouncing high expected profit.

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Open-Pit Mining with Uncertainty: A Conditional Value-at-Risk Approach

Optimization Theory, Decision Making, and Operations Research Applications - Springer Proceedings in Mathematics & Statistics ◽

10.1007/978-1-4614-5134-1_8 ◽

2012 ◽

pp. 117-139 ◽

Cited By ~ 4

Author(s):

Henry Amankwah ◽

Torbjörn Larsson ◽

Björn Textorius

Keyword(s):

At Risk ◽

Value At Risk ◽

Open Pit ◽

Conditional Value At Risk ◽

Open Pit Mining ◽

Risk Approach

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EFFECTS OF MULTIPLE CRITERIA ON PORTFOLIO OPTIMIZATION

International Journal of Information Technology & Decision Making ◽

10.1142/s0219622014500047 ◽

2014 ◽

Vol 13 (01) ◽

pp. 77-99 ◽

Cited By ~ 6

Author(s):

TUNCER ŞAKAR CEREN ◽

MURAT KÖKSALAN

Keyword(s):

At Risk ◽

Portfolio Optimization ◽

Decision Maker ◽

Value At Risk ◽

Efficient Frontier ◽

Conditional Value At Risk ◽

Computational Studies ◽

Expected Return ◽

Risk Criteria ◽

Return Variance

We study the effects of considering different criteria simultaneously on portfolio optimization. Using a single-period optimization setting, we use various combinations of expected return, variance, liquidity and Conditional Value at Risk criteria. With stocks from Borsa Istanbul, we make computational studies to show the effects of these criteria on objective and decision spaces. We also consider cardinality and weight constraints and study their effects on the results. In general, we observe that considering alternative criteria results in enlarged regions in the efficient frontier that may be of interest to the decision maker. We discuss the results of our experiments and provide insights.

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Application of Portfolio Theory Based on CVaR in Determining Optimal Spinning Reserve with Consideration of Load and Wind Power Uncertainties

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.724-725.649 ◽

2013 ◽

Vol 724-725 ◽

pp. 649-654

Author(s):

Jun Li Wu ◽

Bu Han Zhang ◽

Zhen Yin Xiao ◽

Kui Wang

Keyword(s):

Power System ◽

Wind Power ◽

Value At Risk ◽

Efficient Frontier ◽

Portfolio Theory ◽

Conditional Value At Risk ◽

Power Prediction ◽

Spinning Reserve ◽

The Cost ◽

Installed Capacity

With the increased installed capacity of wind power in power system, determining optimal spinning reserve capacity is one of the most important problems in operation of electricity power system. CVaR (conditional value at risk) is introduced to calculate the risk of the cost associated with load shed and abandoning wind power with the consideration of load and wind power prediction uncertainties. Portfolio theory based on CVaR is used to build the Cost-CVaR model. Efficient frontier, which can support the system operators (SO) with the decision of optimal spinning reserve, can be obtained by solving the Cost-CVaR model. The analysis of RTS example can demonstrate the usefulness and efficiency of the model.

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Bi-objective facility location under uncertainty with an application in last-mile disaster relief

Annals of Operations Research ◽

10.1007/s10479-021-04422-4 ◽

2021 ◽

Author(s):

Najmesadat Nazemi ◽

Sophie N. Parragh ◽

Walter J. Gutjahr

Keyword(s):

Real World ◽

Value At Risk ◽

Demand Uncertainty ◽

Disaster Relief ◽

Pareto Frontier ◽

Data Uncertainty ◽

Conditional Value At Risk ◽

Two Stage ◽

Last Mile ◽

Conflicting Objectives

AbstractMultiple and usually conflicting objectives subject to data uncertainty are main features in many real-world problems. Consequently, in practice, decision-makers need to understand the trade-off between the objectives, considering different levels of uncertainty in order to choose a suitable solution. In this paper, we consider a two-stage bi-objective single source capacitated model as a base formulation for designing a last-mile network in disaster relief where one of the objectives is subject to demand uncertainty. We analyze scenario-based two-stage risk-neutral stochastic programming, adaptive (two-stage) robust optimization, and a two-stage risk-averse stochastic approach using conditional value-at-risk (CVaR). To cope with the bi-objective nature of the problem, we embed these concepts into two criterion space search frameworks, the $$\epsilon $$ ϵ -constraint method and the balanced box method, to determine the Pareto frontier. Additionally, a matheuristic technique is developed to obtain high-quality approximations of the Pareto frontier for large-size instances. In an extensive computational experiment, we evaluate and compare the performance of the applied approaches based on real-world data from a Thies drought case, Senegal.

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Cryptocurrency Portfolio Selection—A Multicriteria Approach

Mathematics ◽

10.3390/math9141677 ◽

2021 ◽

Vol 9 (14) ◽

pp. 1677

Author(s):

Zdravka Aljinović ◽

Branka Marasović ◽

Tea Šestanović

Keyword(s):

At Risk ◽

Standard Deviation ◽

Portfolio Selection ◽

Value At Risk ◽

Selection Process ◽

Efficient Frontier ◽

Conditional Value At Risk ◽

Optimal Portfolios ◽

Promethee Ii ◽

Proposed Model

This paper proposes the PROMETHEE II based multicriteria approach for cryptocurrency portfolio selection. Such an approach allows considering a number of variables important for cryptocurrencies rather than limiting them to the commonly employed return and risk. The proposed multiobjective decision making model gives the best cryptocurrency portfolio considering the daily return, standard deviation, value-at-risk, conditional value-at-risk, volume, market capitalization and attractiveness of nine cryptocurrencies from January 2017 to February 2020. The optimal portfolios are calculated at the first of each month by taking the previous 6 months of daily data for the calculations yielding with 32 optimal portfolios in 32 successive months. The out-of-sample performances of the proposed model are compared with five commonly used optimal portfolio models, i.e., naïve portfolio, two mean-variance models (in the middle and at the end of the efficient frontier), maximum Sharpe ratio and the middle of the mean-CVaR (conditional value-at-risk) efficient frontier, based on the average return, standard deviation and VaR (value-at-risk) of the returns in the next 30 days and the return in the next trading day for all portfolios on 32 dates. The proposed model wins against all other models according to all observed indicators, with the winnings spanning from 50% up to 94%, proving the benefits of employing more criteria and the appropriate multicriteria approach in the cryptocurrency portfolio selection process.

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Analysis of Risk Transmission from Generation Right Trading to Generation Company Profit

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.403-408.2856 ◽

2011 ◽

Vol 403-408 ◽

pp. 2856-2860 ◽

Cited By ~ 2

Author(s):

Xian Li ◽

Cun Bin Li ◽

Gong Shu Lu

Keyword(s):

At Risk ◽

Value At Risk ◽

Power Plants ◽

Efficient Frontier ◽

Conditional Value At Risk ◽

Important Impact ◽

Generation Company

With the booming of generation right trade(GRT) market, the GRT risk will exert an increasingly important impact on profit of power plants. Hence, Two conditional value at risk (CVaR) models are built for generation rights sellers and buyers respectively. Then, different proportion constraints are set to discuss the influence of GRT. A conclusion can be drawn that the variances of the ratio of generation right power amount may lead to different amount of distribution in different markets as well as the changes of the efficient frontier curves.

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Forecasting Efficient Risk/Return Frontier for Equity Risk with a KTAP Approach—A Case Study in Milan Stock Exchange

Symmetry ◽

10.3390/sym11081055 ◽

2019 ◽

Vol 11 (8) ◽

pp. 1055 ◽

Cited By ~ 6

Author(s):

Marina Dolfin ◽

Leone Leonida ◽

Eleonora Muzzupappa

Keyword(s):

Value At Risk ◽

Stock Exchange ◽

Stochastic Game ◽

Optimization Theory ◽

Efficient Frontier ◽

Conditional Value At Risk ◽

Risk Return ◽

Equity Risk ◽

Research Perspectives

We introduce and discuss a dynamics of interaction of risky assets in a portfolio by resorting to methods of statistical mechanics developed to model the evolution of systems whose microscopic state may be augmented by variables which are not mechanical. Statistical methods are applied in the present paper in order to forecast the dynamics of risk/return efficient frontier for equity risk. Specifically, we adopt the methodologies of the kinetic theory for active particles (KTAP) with stochastic game-type interactions and apply the proposed model to a case study analyzing a subset of stocks traded in Milan Stock Exchange. In particular, we evaluate the efficient risk/return frontier within the mean/variance portfolio optimization theory for 13 principal components of the Milan Stock Exchange and apply the proposed kinetic model to forecast its short-term evolution (within one year). The model has the aim to pave the way to many different research perspectives and applications discussed eventually in the paper. In particular, the case of efficient frontier obtained by minimizing the Conditional Value-at-Risk (CVaR) is introduced and a preliminary result is proposed.

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Cryptocurrencies and portfolio diversification in an emerging market

China Finance Review International ◽

10.1108/cfri-06-2021-0123 ◽

2022 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Lehlohonolo Letho ◽

Grieve Chelwa ◽

Abdul Latif Alhassan

Keyword(s):

Market Economy ◽

Value At Risk ◽

Emerging Market ◽

Efficient Frontier ◽

Conditional Value At Risk ◽

Portfolio Risk ◽

Investment Portfolio ◽

Content Type ◽

The Mean ◽

Mean Variance

PurposeThis paper examines the effect of cryptocurrencies on the portfolio risk-adjusted returns of traditional and alternative investments within an emerging market economy.Design/methodology/approachThe paper employs daily arithmetic returns from August 2015 to October 2018 of traditional assets (stocks, bonds, currencies), alternative assets (commodities, real estate) and cryptocurrencies. Using the mean-variance analysis, the Sharpe ratio, the conditional value-at-risk and the mean-variance spanning tests.FindingsThe paper documents evidence to support the diversification benefits of cryptocurrencies by utilising the mean-variance tests, improving the efficient frontier and the risk-adjusted returns of the emerging market economy portfolio of investments.Practical implicationsThis paper firmly broadens the Modern Portfolio Theory by authenticating cryptocurrencies as assets with diversification benefits in an emerging market economy investment portfolio.Originality/valueAs far as the authors are concerned, this paper presents the first evidence of the effect of diversification benefits of cryptocurrencies on emerging market asset portfolios constructed using traditional and alternative assets.

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