Risk-neutral Approach Research Articles

Pre-disaster allocation and post-disaster dispatch strategies of power emergency resources for resilience enhancement of distribution networks

With the frequent occurrence of large-scale power outages caused by extreme disasters, coordinated dispatch of power emergency resources (PERs) and repair crews (RCs) has gradually become an essential method to enhance the resilience of distribution networks (DNs). Previous works solve this coordinated dispatch problem in a risk-neutral approach with the assumption that the supply of power repair materials (PRMs) is still fully available after the disaster. However, growing evidence indicates that certain extreme disasters may lead to limited availability of PERs in the DN, rendering risk-neutral decision making impractical. To fill this gap, this paper proposes a resilience-oriented PERs pre-disaster allocation and post-disaster dispatch strategy in a risk-averse manner. In the pre-disaster prevention process, a two-stage distributionally robust optimization (DRO) model based on mean-CVaR is developed, considering the uncertainties of both system damage and PERs demands, along with the decision maker's preference for risk. In the post-disaster restoration process, a collaborative spatio-temporal dispatching model for PERs and RCs with the goal of minimizing outage losses is established. To tackle the computational challenges associated with PRMs allocation based on DRO, robust counterpart transformation and dual theory are utilized. Case studies are conducted using a real world modified 118-bus distribution network. In comparative analysis, five control groups are established to validate the necessity to consider the limited supply of PRMs and the risk-averse attitude of decision makers in enhancing DNs resilience.

Comparison of evolutionary algorithms for solving risk-based energy resource management considering conditional value-at-risk analysis

Energy management systems must evolve due to the widespread use of distributed energy resources in modern society. In fact, with the current high penetration of renewables and other resources like electric vehicles, the challenge of managing energy resources becomes more difficult. Uncertainty and unpredictability from distributed resources open the door for unique undesirable situations, often known as extreme events. Despite the low likelihood of occurrence, such severe events represent a significant risk to an aggregator’s resource management, for example. In this paper, we propose a day-ahead energy resource management model for an aggregator in a 13-bus distribution network with high penetration of distributed energy resources. In the proposed model, we consider a risk-based mechanism through the conditional value-at-risk method for risk measurement of these extreme events. Due to the complexity of the model, we also propose the use of evolutionary algorithms, a set of stochastic search algorithms, to find near-optimal solutions to the problem. Results show that implementing risk-averse strategies reduces the cost of the worst scenario and scheduling. From the tested algorithms, ReSaDE provides the solutions with the lowest cost, which is an improvement from previous work, and a reduction of around 13% in the worst-scenario costs comparing a risk-neutral approach to a risk-averse approach.

A risk-neutral approach to the RAROC method of loan pricing using account-level data

PurposeThis paper has used account-level data of corporate and retail borrowers, assessed their credit risk through the risk-neutral principle and examined its implication on loan pricing.Design/methodology/approachIt derives the capital charge and credit risk-premium for expected and unexpected losses through a risk-neutral approach. It estimates the risk-adjusted return on capital as the pricing principle for loans. Using GMM regression, the article has assessed the determinants of risk-based pricing.FindingsIt has been found that risk-premium is not reflected in the current loan pricing policy as per Basel II norms. However, the GMM estimation on RAROC can price risk premium and probability of default, LGD, risk weight, bank beta and capital adequacy, which are the prime determinants of loan pricing. The average RAROC for retail loans is more than that of corporate loans despite the same level of risk capital requirement for both categories of loans. The robustness tests indicate that the RAROC method of loan pricing and its determinants are consistent against the time and type of borrowers.Research limitations/implicationsThe RAROC method of pricing effectively assesses the inherent risk associated with loans. Though the empirical findings are confined to the sample bank, the model can be used for any bank implementing the Basel principle of risk and capital assessments.Practical implicationsThe article has developed and validated the model for estimating RAROC, as per Basel II guidelines, for loan pricing that any bank can use.Social implicationsIt has developed the risk-based loan pricing model for retail and corporate borrowers. It has significant practical utility for banks to manage their risk, reduce their losses and productively utilise the public deposits for societal developments.Originality/valueThe article empirically validated the risk-neutral pricing principle using a unique 1,520 retail and corporate borrowers dataset.

Reverse Logistics Network Design under Disruption Risk for Third-Party Logistics Providers

Reverse logistics is attracting attention due to the increasing concerns over environmental issues and the important economic impacts. The design of a reverse logistics network is a major strategic problem in the field of reverse logistics. As cost pressures in product returns continue to mount, a growing number of manufacturers have begun to outsource reverse logistics operations to third-party logistics (3PL) providers. On the other hand, considering disruption risks caused by natural or man-made factors in the reverse logistics network design is inevitable. This paper studies third-party reverse logistics network designs under uncertain disruptions. The problem is formulated as a risk-averse two-stage stochastic programming model with a mean risk objective. Two types of risk measures, value at risk (VaR) and conditional value at risk (CVaR), were examined, respectively. Finally, the sensitivity analysis of the model was carried out. The validity of the mean risk criteria is proved by comparison with risk-neutral approach. Moreover, the performance of the proposed model was examined by stochastic measures.

Less-expensive long-term annuities linked to mortality, cash and equity

AbstractThis paper proposes a shift in the valuation and production of long-term annuities, away from the classical risk-neutral methodology towards a methodology using the real-world probability measure. The proposed production method is applied to three examples of annuity products, one having annual payments linked to a mortality index and the savings account and the others having annual payments linked to a mortality index and an equity index with a guarantee that is linked to the same mortality index and the savings account. Out-of-sample hedge simulations demonstrate the effectiveness of the proposed less-expensive production method. In contrast to classical risk-neutral production, which revolves around the savings account as reference unit, the long-term best-performing portfolio, the numéraire portfolio of the equity market, is employed as the fundamental reference unit in the production of the annuity. The numéraire portfolio is the strictly positive, tradable portfolio that when used as denominator or benchmark makes all benchmarked non-negative portfolios supermartingales. Under real-world valuation, the initial benchmarked value of a benchmarked contingent claim equals its real-world conditional expectation. The proposed real-world valuation and production can lead to significantly lower values of long-term annuities and their less-expensive production than suggested by the risk-neutral approach.

Single-stage gradient-based stellarator coil design: stochastic optimization

We extend the single-stage stellarator coil design approach for quasi-symmetry on axis from (Giuliani et al 2020) to additionally take into account coil manufacturing errors. By modeling coil errors independently from the coil discretization, we have the flexibility to consider realistic forms of coil errors. The corresponding stochastic optimization problems are formulated using a risk-neutral approach and risk-averse approaches. We present an efficient, gradient-based descent algorithm which relies on analytical derivatives to solve these problems. In a comprehensive numerical study, we compare the coil designs resulting from deterministic and risk-neutral stochastic optimization and find that the risk-neutral formulation results in more robust configurations and reduces the number of local minima of the optimization problem. We also compare deterministic and risk-neutral approaches in terms of quasi-symmetry on and away from the magnetic axis, and in terms of the confinement of particles released close to the axis. Finally, we show that for the optimization problems we consider, a risk-averse objective using the conditional value-at-risk leads to results which are similar to the risk-neutral objective.

Bi-objective stochastic model for the design of biofuel supply chains incorporating risk

The design of a biofuel supply chain network involves multiple uncertainty sources such as the biomass supply and quality. Most of the previous works took a risk-neutral approach by modeling this problem as two-stage stochastic formulation. However, most decision makers are not risk-neutral and a better understanding of the risk involved is germane. This study proposes a bi-objective two-stage stochastic optimization model that considers the expected total cost and the CVaR as objective functions. The first stage determines the location of biorefineries, and the second stage decides the flow between suppliers (counties) and biorefineries. We assume as non deterministic two features of switchgrass (biomass), the ash and moisture contents. To solve this problem, a hybrid method based on a Simulated Annealing algorithm and the augmented ε-constraint method is developed and tested using a realistic large-scale case study in the state of Texas. Based on the experimental results, we observe that the CVaR is not a suitable risk measure when the problem involves a third party because the cost of third-party does not imply risk for the decision makers (biorefinery owner). Therefore, the PVaR model is more suitable for the nature of this problem since PVaR includes the risk inherent to the third party in case this entity is not able to fulfill the demand of biofuel not covered by the supply chain network. As a result, we reformulate the original model by replacing the CVaR by PVaR to create a tailor-made formulation for the bi-objective two-stage stochastic programming problem including third party biofuel suppliers. Compared to existing solution procedures, the proposed hybrid method has merits in terms of computational burden and solution quality. Computational experiments show that the lower the confidence level in the third party (that is, a less reliable supplier needed to meet the bioethanol demand), the higher the expected costs and the PVaR (risk) for the supply chain design.

Two-stage risk-averse stochastic programming approach for multi-item single source ordering problem: CVaR minimisation with transportation cost

Integrating inventory and transportation decisions is vital in supply chain management and can enable decision-makers to achieve competitive advantages. This study considers a multi-item replenishment problem (MIRP) with a piece-wise linear transportation cost under demand uncertainty, which usually occurs both in retail and production environment when several items must be ordered from a single supplier. Conventionally, two-stage stochastic programming formulation is risk-neutral, and it lacks robustness in the presence of high data variability. Hence, we introduce the Conditional Value at Risk (CVaR) approach for MIRP. Additionally, we deploy both single and multi-cut L-shaped and the sample average approximation method to circumvent the computational complexity to solve large-scale instances. The data-driven simulation study is used to benchmark the results from deterministic, risk-neutral, and risk-averse stochastic models. The results indicate that under higher data variations, the risk-averse model provides better perspectives for a decision-maker. The results show a 40–50% reduction in lost sales with marginal growth in total cost while considering CVaR instead of a risk-neutral approach.

Designing a closed-loop supply chain for reusable packaging materials: A risk-averse two-stage stochastic programming model using CVaR

Reusable packaging material (RPM) provide a circular and sustainable way of transporting parts/products safely along the various stages of supply chain. In the present work, we study a multi-echelon closed-loop supply chain network design problem for wooden RPMs. Initially, a mixed-integer programming model under deterministic setting is proposed to determine the optimal configuration of the manufacturing facilities and distribution centers of RPMs. Further, a risk-averse two-stage stochastic programming model is developed to incorporate the uncertainties associated with the demand, initial inventory and level of reusability of the RPMs. The developed model utilizes conditional-value-at-risk (CVaR) as risk measure since it provides more robust solutions compared to a risk-neutral approach in presence of uncertainty. The applicability of the model is explained using a real-life example of the prevalent supply chain of wooden pallets in several automobile manufacturers and their suppliers in India. The results suggest trade-off among various cost components such as fixed cost of opening facilities and capacity installation, manufacturing, acquisition, refurbishing, and environmental cost. Several managerial insights are drawn by carrying out sensitivity analysis of deterministic model and running the stochastic model with different values of CVaR parameters. Finally, we present numerical results to discuss how incorporating a risk measure affects the computational performance and solution of the CVaR model.

Stochastic Last-Mile Delivery with Crowd-Shipping and Mobile Depots

This paper proposes a two-tier last-mile delivery model that optimally selects mobile depot locations in advance of full information about the availability of crowd-shippers and then transfers packages to crowd-shippers for the final shipment to the customers. Uncertainty in crowd-shipper availability is incorporated by modeling the problem as a two-stage stochastic integer program. Enhanced decomposition solution algorithms including branch-and-cut and cut-and-project frameworks are developed. A risk-averse approach is compared against a risk-neutral approach by assessing conditional-value-at-risk. A detailed computational study based on the City of Toronto is conducted. The deterministic version of the model outperforms a capacitated vehicle routing problem on average by 20%. For the stochastic model, decomposition algorithms usually discover near-optimal solutions within two hours for instances up to a size of 30 mobile depot locations, 40 customers, and 120 crowd-shippers. The cut-and-project approach outperforms the branch-and-cut approach by up to 85% in the risk-averse setting in certain instances. The stochastic model provides solutions that are 3.35%–6.08% better than the deterministic model, and the improvements are magnified with increased uncertainty in crowd-shipper availability. A risk-averse approach leads the operator to send more mobile depots or postpone customer deliveries to reduce the risk of high penalties for nondelivery.

Calibration to FX triangles of the 4/2 model under the benchmark approach

We calibrate a novel multifactor stochastic volatility model that includes as special cases the Heston-based model of De Col et al. (J Bank Finance 37(10):3799–3818, 2013) and the 3/2-based model of Baldeaux et al. (J Bank Finance 53:34–48, 2015). Using a dataset on vanilla option quotes in a triangle of currencies, we find that the risk neutral approach typically fails for the calibrated model, in line with the results of Baldeaux et al. (2015).

Irreducible Risks: Fallacy of Risk-Neutral Approach to Options

This paper compares two approaches to options: (1) Risk-Aware Approach, and (2) Risk-Neutral Approach. The risk-aware approach requires a probabilistic specification of the underlying’s returns, addressing higher than second moments, as hedging errors are singularly dependent on the excess kurtosis of the returns. Becoming risk-aware requires explicitly assessing hedge slippage of a hedging strategy to attempt option replication. In contrast, the risk-neutral tautology sets the option price equal to an expectation of option payoff under a risk-neutral probability that is inferred from option prices and under which the asset does not expect to accrete/deplete wealth. In the presence of irreducible risks, while a risk-neutral probability measure may be fit to observed option prices, it does not inform about the partitioning between expected attempted replication costs and compensation for irreducible risks. In segmented option markets with distinct risk premiums such a risk-neutral probability measure fails to exist.

Revisiting the Risk-Neutral Approach to Optimal Policyholder Behavior: A Study of Withdrawal Guarantees in Variable Annuities

Policyholder exercise behavior presents an important risk factor for pricing Variable Annuities. However, approaches presented in the literature—building on value-maximizing strategies akin to pricing American options—do not square with observed price and exercise patterns for popular withdrawal guarantees. We show that including taxes into the valuation closes this gap between theory and practice. In particular, we develop a subjective risk-neutral valuation methodology that takes into consideration differences in the tax structure between investment opportunities. We demonstrate that accounting for tax advantages significantly affects the value of the guarantees and produces results that are in line with empirical patterns.

Contractor's Attitude towards Risk and Risk Management in Construction in Two Western Provinces of Vietnam

Risk management is an important task in construction management that helps the contractor to actively identify, evaluate, control, and minimize negative impacts of risks on the project, thereby ensuring its effectiveness. People involved in the construction industry need to be well - equipped with information and knowledge to manage risks adequately and systematically. The purpose of this research is to explore the attitude towards risk and risk management in construction projects of the Vietnamese construction industry, with emphasis on the perspective of contractors. The research data are collected through a questionnaire associated with in-depth semi-structured interviews. The results indicate that the perception of risk within the Vietnamese construction industry includes both threats and opportunities. The majority of professionals in the industry have a risk-neutral approach, contrary to previous research. The importance of implementing effective risk management is shared, in the planning and production phase while risk identification was perceived to be the most important out of the four core processes.

Incorporating Production Task Scheduling in Energy Management of an Industrial Microgrid: A Regret-Based Stochastic Programming Approach

In this paper, a regret-based risk-averse stochastic production task and energy management (PTEM) model for industrial microgrid is proposed, which is applied to a battery manufacturing plant (BMP) microgrid. We incorporate production task scheduling with production constraints in the energy management of industrial microgrid. The general PTEM of industrial microgrids is analyzed and the production processes and energy requirements of a BMP multi-energy microgrid prosumer are presented, in which thermostatically controlled loads (TCLs) in buildings are considered. Then, the regret-based risk-averse PTEM model is formulated as a mixed-integer linear programming (MILP) problem based on stochastic programming considering uncertainties of day-ahead electricity market price and photovoltaic (PV) power output. Conditional value-at-risk (CVaR) is introduced for risk control and utilized for minimizing the expected regret. Numerical studies are carried out to validate the proposed model by comparing with risk-neutral approach and deterministic model based on real market prices from PJM electricity market. The results show that the proposed PTEM approach is effectively risk-averse. In addition, the impacts of total target production task and risk-control parameter on expected cost and regret are analyzed.

Improving the option pricing performance of GARCH models in inefficient market

Understanding the relation between option pricing and market efficiency is important. Indeed, emphasizing this relation generates new insights that are appropriate in practice. These insights give a better understanding of the current limitations of the option pricing and hedging methods. This article thus aims to improve the performance of the option pricing approach. To start, the relation between the option pricing methodology and the informational market efficiency was discussed. It is, therefore, useful, before proceeding to apply the standard risk-neutral approach, to check the efficiency assumption. New modified GARCH processes were used to model the dynamics of the asset returns in the option pricing framework. The new considered approaches allow describing the dynamic of returns when the market is inefficient. Using real data on CAC 40 index, the performance of different models as a function of maturity and moneyness was studied. The in-sample analysis, interested in the stability of the pricing models across time, showed that the new approach, developed under the affine GARCH process, is the most accurate. The study of the out-of-sample performance, which aims to evaluate the forecasting ability of different approaches, confirmed the results of the in-sample analysis. For the optional portfolio hedging, always the best hedging approach is that obtained under the affine GARCH model. After a regression study, it was found that the difference between theoretical and observed option values can be explained by factors, which are not taken into account in the proposed pricing formulae.

Gain-Scheduled Mean-Field-Type Control for a Non-Linear Continuous Stirred Tank Reactor

We present the design of a Gain-Scheduled Mean-Field-Type Control (GS-MFTC) for a non-linear Continuous Stirred Tank Reactor (CSTR). The MFTC controllers belong to a class of stochastic control techniques considering the distribution of the system states, and control inputs, while minimizing the variance of both variables of interest. The underlying risk-aware control problem is solved explicitly for the infinite horizon in order to determine the required gains composing the feedback control input law. We present both the risk-neutral approach involving the first and second moment (mean and variance terms), and the risk-sensitive approach involving higher-order terms.

The Difference between Modigliani–Miller and Miles–Ezzell and its Consequences for the Valuation of Annuities

This paper addresses the differences between the Modigliani-Miller [M&M] model (1958, 1963) and the Miles-Ezzell [M&E] model (1980, 1985). The main difference between these two models concerns the stochasticity of the free cash flows. While M&M assume a strictly stationary process, M&E’s process is a martingale. However, this subtle difference has not been fully exposed, and previous literature has produced partly erroneous statements or inconsistent valuation models. Therefore, the main objective of this paper is to illustrate and accentuate the effect of these two mutually exclusive stochastic processes on the timely behavior of cash flows, discount rates, and values of the firm, equity, debt and tax shield. For this purpose, we perform a numerical experiment that allows the determination of values and discount rates by means of the risk-neutral approach. We show that in the M&E model, all cash flows and values are path-dependent, while they are not in M&M’s world. Furthermore, in M&E’s model all discount rates are time-invariant, except for the discount rate applied to tax shields, which depends on the lifetime of the cash flows. Contrary, in the M&M setup, all discount rates change across time, except for the constant discount rate of the tax shield. This has consequences for the applicability of the well-known present-value formula for annuities and for building consistent valuation models for both finite and perpetual cash flows.

Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations

In this article, we first provide a survey of the exponential option pricing models and show that in the framework of the risk-neutral approach, they are governed by the space-fractional diffusion equation. Then, we introduce a more general class of models based on the space-time-fractional diffusion equation and recall some recent results in this field concerning the European option pricing and the risk-neutral parameter. We proceed with an extension of these results to the class of exotic options. In particular, we show that the call and put prices can be expressed in the form of simple power series in terms of the log-forward moneyness and the risk-neutral parameter. Finally, we provide the closed-form formulas for the first and second order risk sensitivities and study the dependencies of the portfolio hedging and profit-and-loss calculations upon the model parameters.

Risk-Constrained Optimal Chiller Loading Strategy Using Information Gap Decision Theory

This paper presents a novel framework for economic cooling load dispatch in conventional water-cooled chillers. Moreover, information gap decision theory (IGDT) is applied to the optimal chiller loading (OCL) problem to find the optimum operating point of the test system in three decision-making modes: (a) risk-neutral approach, (b) risk-aversion or robustness approach, and (c) risk-taker or opportunistic approach. In the robustness mode of the IGDT-based OCL problem, the system operator enters a desired energy cost value in order to find the most appropriate loading points for the chillers so that the total electricity procurement cost over the study horizon is smaller than or equal to this critical value. Meanwhile, the cooling load increase is maximized to the highest possible level to find the most robust performance of the benchmark grid with respect to the overestimated load. Similarly, the risk-taker optimization method finds the on/off status and the partial load ratio (PLR) of the chillers in order to keep the total energy cost as low as the given cost function. In addition, the minimum value of cooling load decrease can be found while satisfying the refrigeration capacity of the chiller and the load-generation balance constraint. Thus, a mixed-integer non-linear programming problem is solved using the branch and reduce optimization (BARON) tool of the generalized algebraic mathematical modeling system (GAMS) for a five-chiller plant, to demonstrate that IGDT is able to find a good solution in robustness/risk-taker OCL problem.