Recent progress in random metric theory and its applications to conditional risk measures

The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introduction,which gives a brief introduction to random metric theory,risk measures and conditional risk measures.Section 2 gives the central framework in random metric theory,topological structures,important examples,the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals.Section 3 gives several important representation theorems for random conjugate spaces.Section 4 gives characterizations for a complete random normed module to be random reflexive.Section 5 gives hyperplane separation theorems currently available in random locally convex modules.Section 6 gives the theory of random duality with respect to the locally L0-convex topology and in particular a characterization for a locally L0-convex module to be L0-pre-barreled.Section 7 gives some basic results on L0-convex analysis together with some applications to conditional risk measures.Finally,Section 8 is devoted to extensions of conditional convex risk measures,which shows that every representable L∞-type of conditional convex risk measure and every continuous Lp-type of convex conditional risk measure(1 ≤ p < +∞) can be extended to an L∞F(E)-type of σ,λ(L∞F(E),L1F(E))-lower semicontinuous conditional convex risk measure and an LpF(E)-type of T,λ-continuous conditional convex risk measure(1 ≤ p < +∞),respectively.

Solving the subset sum problem by the quantum Ising model with variational quantum optimization based on conditional values at risk

The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or scheduling,and integer partitions.An accurate search algorithm with polynomial time complexity has not been found,which makes it challenging to be solved on classical computers.To effectively solve this problem,we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at risk.The proposed model needs only n qubits to encode 2ndimensional search space,which can effectively save the encoding quantum resources.The model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise,and it is convenient to be deployed in the Noisy Intermediate Scale Quantum era.We investigate the effects of the scalability,the variational ansatz type,the variational depth,and noise on the model.Moreover,we also discuss the performance of the model under different conditional values at risk.Through computer simulation,the scale can reach more than nine qubits.By selecting the noise type,we construct simulators with different QVs and study the performance of the model with them.In addition,we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum problem.This model provides a new perspective for solving the subset sum problem.

A Framework for Modern Risk-Informed Root Cause Analysis Process

The paper discusses the framework for a risk-informed root cause analysis process.Such process enables scaling of the analysis performed based on the risk associated with the undesired event or condition,thereby creating tiers of analysis where the greater the risk,the more sophisticated the analysis.In a risk-informed root cause analysis process,a situation is normally not analyzed at a level less than what actually occurred.However,a situation may be investigated as though the consequence were greater than actually happened,especially if only slight differences in circumstances could result in a significantly higher consequence.While operational events or safety issues are normally expected to result only with negligible or marginal actual consequences,many of those would actually have certain potential to develop or propagate into catastrophic events.This potential can be expressed qualitatively or quantitatively.Risk-informing of root cause analysis relies on mapping the event or safety issue into a risk matrix which,traditionally,is a two-dimensional probability-consequence matrix.A new concept employed in the risk matrix for root cause analysis is that,while the probability reflects the observed or expected range of values(retaining,thus,its“traditional”meaning),the consequence reflects not only the observed or materialized impact(such as failure of equipment)but,also,its potential to propagate or develop into highly undesirable final state.The paper presents main elements of risk-informed root cause analysis process and discusses qualitative and quantitative aspects and approaches to determination of risk significance of operational events or safety issues.

Market Risk Evaluation on Single Futures Contract:SV-CVaR Model and Its Application on Cu00 Data

A new stochastic volatility（SV）method to estimate the conditional value at risk（CVaR）is put forward.Firstly,it makes use of SV model to forecast the volatility of return.Secondly,the Markov chain Monte Carlo（MCMC）simulation and Gibbs sampling have been used to estimate the parameters in the SV model.Thirdly,in this model,CVaR calculation is immediate.In this way,the SV-CVaR model overcomes the drawbacks of the generalized autoregressive conditional heteroscedasticity value at risk（GARCH-VaR）model.Empirical study suggests that this model is better than GARCH-VaR model in this field.

Health risk of whole body vibration in mining trucks during various operational conditions

Mining machineries are generally exposed to intensive vibrations in harsh mining environment. If vibrations are beyond the tolerable limit, the machine and its operator health will be under the risk. In this work, the vibration of a mining truck at different operational conditions are simulated and discussed. To achieve this aim, three haul roads with low, medium and poor qualities are considered based on the ISO standard. Accordingly, the vibration of a mining truck in different speeds, payload and distribution qualities of materials in the dump body are evaluated in each haul road quality using Trucksim software. The simulation results with statistical discussions indicate that the truck speed and the materials distribution quality have significant effects on the root mean square(RMS) of vertical vibrations. However, the effect of the payload is not considerable on the RMS. Moreover, the accumulation of materials on the rear side of the truck dump body is efficient on the vibrational health risk.

Overcoming Investment Risks Chinese investors need to thoroughly understand local conditions before investing in Africa

With abundant labor resources and the increase in policy sup port for economie development and loreign investment, Africa is becoming a new sought-after destination for investment by multinational companics.

Risk Constrained Self-scheduling of AA-CAES Facilities in Electricity and Heat Markets:A Distributionally Robust Optimization Approach

Advanced adiabatic compressed air energy storage(AA-CAES)has the advantages of large capacity,long service time,combined heat and power generation(CHP),and does not consume fossil fuels,making it a promising storage technology in a low-carbon society.An appropriate self-scheduling model can guarantee AA-CAES’s profit and attract investments.However,very few studies refer to the cogeneration ability of AA-CAES,which enables the possibility to trade in the electricity and heat markets at the same time.In this paper,we propose a multimarket self-scheduling model to make full use of heat produced in compressors.The volatile market price is modeled by a set of inexact distributions based on historical data through-divergence.Then,the self-scheduling model is cast as a robust risk constrained program by introducing Stackelberg game theory,and equivalently reformulated as a mixed-integer linear program(MILP).The numerical simulation results validate the proposed method and demonstrate that participating in multienergy markets increases overall profits.The impact of uncertainty parameters is also discussed in the sensibility analysis.

Application of decision tree to selection of MTBM for adverse geological conditions

So many potential risks can be identifed for application of trenchless technology especially using microtunneling methods.Unexpected changes in ground conditions,such as encountering boulders,tree roots,ground water and man-made structures such as old foundations are the principal geotechnical risks,which affect the selection of an appropriate microtunnel boring machine.On the other hand,the performance of each microtunneling technique will differ while encountering such conditions.Hence,predicting the potential hazards provides a better safety and risk management plan.In this study,a couple of potentially hazardous situation,which are commonly associated with ground conditions,were identifed and investigated.A decision tree aid methodology was proposed based on geotechnical risk assessment for selection of proper microtunneling technique.Based on the approach the most appropriate microtunneling technique has the minimum risk level either before or after hazards mitigation measures.In order to check the effciency of the approach in practice,selection of microtunnel boring machine for Hamadan sewerage pipeline project was evaluated.Accordingly,an earth pressure balance(EPB)MTBM was selected for the project.

Conditional coherent risk measures and regime-switching conic pricing

This paper introduces and represents conditional coherent risk measures as essential suprema of conditional expectations over a convex set of probability measures and as distorted expectations given a concave distortion function.A model is then developed for the bid and ask prices of a European-type asset by a conic formulation.The price process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend on a Markov chain.The bid and ask prices of a European-type asset are then characterized using conic quantization.

Measuring Real Capital Adequacy in Extreme Economic Conditions： An Examination of the Swiss Banking Sector

The global financial crisis （GFC） has placed the creditworthiness of banks under intense scrutiny. In particular, capital adequacy has been called into question. Current capital requirements make no allowance for capital erosion caused by movements in the market value of assets. This paper examines default probabilities of Swiss banks under extreme conditions using structural modeling techniques. Conditional Value at Risk （CVaR） and Conditional Probability of Default （CPD） techniques are used to measure capital erosion. Significant increase in Probability of Default （PD） is found during the GFC period. The market asset value based approach indicates a much higher PD than external ratings indicate. Capital adequacy recommendations are formulated which distinguish between real and nominal capital based on asset fluctuations.

Risk-based Two-stage Optimal Scheduling of Energy Storage System with Second-life Battery Units

With the growing adoption of Electrical Vehicles(EVs),it is expected that a large number of on-board Li-ion batteries will be retired from EVs in the near future.Retired batteries will typically retain 80%of their initial capacities and can be recycled as second life batteries(SLBs).Although the capital costs of SLBs are much cheaper,their operational reliability is an important concern since used batteries may suffer from a higher failure rate.This paper aggregates brand new batteries and SLBs together to improve power system’s operating performance with renewable energy resources.In the context of a day-ahead and intra-day dispatch framework,a two-stage coordinated optimal scheduling method is proposed.Specifically,the energy cost of brand-new batteries and SLBs is calculated based on detailed battery degradation model,and the reliability of batteries is modeled based on the Weibull distribution.Moreover,Conditional value at risk(CVaR)criterion is applied to evaluate the risk induced by intermittent renewable power output,load demand variation and SLBs failure probability.Simulation tests demonstrate the effectiveness of the proposed method.

Bi-level Multi-leader Multi-follower Stackelberg Game Model for Multi-energy Retail Package Optimization

In the competitive energy market,energy retailers are facing the uncertainties of both energy price and demand,which requires them to formulate reasonable energy purchasing and selling strategies for improving their competitiveness in this market.Particularly,the attractive multi-energy retail packages are the key for retailers to increase their benefit.Therefore,combined with incentive means and price signals,five types of multi-energy retail packages such as peak-valley time-of-use(TOU)price package and day-night bundled price package are designed in this paper for retailers.The iterative interactions between retailers and end-users are modeled using a bi-level model of stochastic optimization based on multi-leader multi-follower(MLMF)Stackelberg game,in which retailers are leaders and end-users are followers.Retailers make decisions to maximize the profit considering the conditional value at risk(CVaR)while end-users optimize the satisfaction of both energy comfort and economy.Besides,a distributed algorithm is proposed to obtain the Nash equilibrium of above MLMF Stackelberg game model while the particle swarm optimization(PSO)algorithm and CPLEX solver are applied to solve the optimization model for each participant(retailer or end-user).Numeral results show that the designed retail packages can increase the overall profit of retailers,and the overall satisfaction of industrial users is the highest while that of residential users is the lowest after game interaction.

Two-stage stochastic programming with robust constraints for the logistics network post-disruption response strategy optimization

Logistics networks (LNs) are essential for the transportation and distribution of goods or services from suppliers to consumers. However, LNs with complex structures are more vulnerable to disruptions due to natural disasters and accidents. To address the LN post-disruption response strategy optimization problem, this study proposes a novel two-stage stochastic programming model with robust delivery time constraints. The proposed model jointly optimizes the new-line-opening and rerouting decisions in the face of uncertain transport demands and transportation times. To enhance the robustness of the response strategy obtained, the conditional value at risk (CVaR) criterion is utilized to reduce the operational risk, and robust constraints based on the scenario-based uncertainty sets are proposed to guarantee the delivery time requirement. An equivalent tractable mixed-integer linear programming reformulation is further derived by linearizing the CVaR objective function and dualizing the infinite number of robust constraints into finite ones. A case study based on the practical operations of the JD LN is conducted to validate the practical significance of the proposed model. A comparison with the rerouting strategy and two benchmark models demonstrates the superiority of the proposed model in terms of operational cost, delivery time, and loading rate.

PRODUCTION PLANNING PROBLEM WITH PRICING UNDER RANDOM YIELD:CVAR CRITERION

In this paper, we address a basic production planning problem with price dependent demand and stochastic yield of production. We use price and target quantity as decision variables to lower the risk of low yield. The value of risk control becomes more important especially for products with short life cycle. This is because, the profit implications of low yield might be unbearable in the short run. We apply Conditional Value at Risk （CVaR） to model the, risk. CVaR measure is a coherent risk measure and thereby having nice conceptual and mathematical underpinnings. It is also widely used in practice. We consider the problem under general demand function and general distribution function of yield and find sufficient conditions under which the problem has a unique local maximum. We also both analytically and numerically analyze the impact of parameter change on the optimal solution. Among our results, we analytically show that with increasing risk aversion, the optimal price increases. This relation is opposite to that of in Newsvendor problem where the uncertainty lies in demand side.

Supply chain network design under uncertainty with new insights from contracts

In this paper, the classical problem of supply chain network design is reconsidered to emphasize the role of contracts in uncertain environments. The supply chain addressed consists of four layers: suppliers, manufacturers, warehouses, and customers acting within a single period. The single owner of the manufacturing plants signs a contract with each of the suppliers to satisfy demand from downstream. Available contracts consist of long-term and option contracts, and unmet demand is satisfied by purchasing from the spot market. In this supply chain, customer demand, supplier capacity, plants and warehouses, transportation costs, and spot prices are uncertain. Two models are proposed here: a risk-neutral two-stage stochastic model and a risk-averse model that considers risk measures. A solution strategy based on sample average approximation is then proposed to handle large scale problems. Extensive computational studies prove the important role of contracts in the design process, especially a portfolio of contracts. For instance, we show that long-term contract alone has similar impacts to having no contracts, and that option contract alone gives inferior results to a combination of option and long-term contracts. We also show that the proposed solution methodology is able to obtain good quality solutions for large scale problems.

A comparison of two no-arbitrage conditions

We give a comparison of two no-arbitrage conditions for the fundamental theorem of asset pricing. The first condition is named as the no free lunch with vanishing risk condition and the second the no good deal condition. We aim to derive a relationship between these two conditions.