Risk-neutral Decision Maker Research Articles

Risk aversion with nothing to lose

In a continuous-time model, a risk-neutral decision-maker chooses the volatility of a state variable and is terminated when the variable falls below a threshold. I provide economically interpretable conditions under which the decision-maker becomes risk averse endogenously and minimizes volatility near termination, even if she faces myopic incentives to gamble for resurrection. The conditions introduce forward-looking incentives to preserve economic rents. I show these conditions are met in a wide range of apparently unrelated models, thus identifying forward-looking rents as a unifying economic mechanism behind endogenous risk aversion. I also provide conditions for the decision-maker to become risk loving endogenously.

Benders Adaptive-Cuts Method for Two-Stage Stochastic Programs

Benders decomposition is one of the most applied methods to solve two-stage stochastic problems (TSSP) with a large number of scenarios. The main idea behind the Benders decomposition is to solve a large problem by replacing the values of the second-stage subproblems with individual variables and progressively forcing those variables to reach the optimal value of the subproblems, dynamically inserting additional valid constraints, known as Benders cuts. Most traditional implementations add a cut for each scenario (multicut) or a single cut that includes all scenarios. In this paper, we present a novel Benders adaptive-cuts method, where the Benders cuts are aggregated according to a partition of the scenarios, which is dynamically refined using the linear program-dual information of the subproblems. This scenario aggregation/disaggregation is based on the Generalized Adaptive Partitioning Method (GAPM), which has been successfully applied to TSSPs. We formalize this hybridization of Benders decomposition and the GAPM by providing sufficient conditions under which an optimal solution of the deterministic equivalent can be obtained in a finite number of iterations. Our new method can be interpreted as a compromise between the Benders single-cuts and multicuts methods, drawing on the advantages of both sides, by rendering the initial iterations faster (as for the single-cuts Benders) and ensuring the overall faster convergence (as for the multicuts Benders). Computational experiments on three TSSPs [the Stochastic Electricity Planning, Stochastic Multi-Commodity Flow, and conditional value-at-risk (CVaR) Facility Location] validate these statements, showing that the new method outperforms the other implementations of Benders methods, as well as other standard methods for solving TSSPs, in particular when the number of scenarios is very large. Moreover, our study demonstrates that the method is not only effective for the risk-neutral decision makers, but also that it can be used in combination with the risk-averse CVaR objective. Funding: Financial support from Agencia Nacional de Investigación y Desarrollo - Chile [FONDECYT 1200809] and STIC-Amsud [STIC19007] is gratefully acknowledged.

Modeling repair demand in existence of a nonstationary installed base

Life cycles of products consist of 3 phases, namely growth, maturity, and decline phases. Modeling repair demand is particularly difficult in the growth and decline stages due to nonstationarity. In this study, we suggest respective stochastic models that capture the dynamics of repair demand in these two phases. We apply our theory to two different operations management problems. First, using the moments of spare parts demand, we suggest an algorithm that selects a parametric distribution from the hypergeometric family (Ord, 1967) for each period in time. We utilize the algorithm in a single echelon inventory control problem. Second, we focus on investment decisions of Original Equipment Manufacturers (OEMs) to extend economic lifetimes of products with technology upgrades. Our results indicate that the second moment is sufficient for growing customer bases, whereas using the third moment doubles the approximation quality of theoretical distributions for a declining customer base. From a cost minimization perspective, using higher moments of demand leads to savings up to 13.6% compared to the single-moment approach. Also, we characterize the optimal investment policy for lifetime extension decisions from risk-neutral and risk-averse perspectives. We find that there exists a critical level of investment cost and installed base size for profitability of lifetime extension for OEMs. From a managerial point of view, we find that a risk-neutral decision maker finds the lifetime extension problem profitable. In contrast, even a slight risk aversion can make the lifetime extension decision economically undesirable.

How Uncertainty Matters Under Risk Neutrality

It is typical in cost-effectiveness analysis to invoke a normative decision-making framework that assumes, as a starting point, that “a quality-adjusted life-year (QALY) is a QALY is a QALY.” The implication of this assumption is that the decision maker is risk neutral and that expected values could be considered sufficiently informative for a given “approve or reject” decision. Nevertheless, it seems intuitive that less uncertainty should be desirable and this has led some to incorporate “real” risk aversion (RA) into cost-effectiveness analysis.We illustrate in this article that RA is not always necessary to justify choosing more over less certain options. We show that for a risk neutral decision maker, greater uncertainty can make the approval of technology less likely in the presence of (1) model nonlinearities, (2) nonlinear opportunity costs, and (3) irreversible costs. We call these cases of “apparent” RA.Incorporating explicit risk preferences into decision making can be challenging; nevertheless, as we show here, it is not necessary to justify caring about uncertainty in approval decisions.

A robust, resilience multi-criteria decision-makingwith risk approach: a case study for renewable energy location.

Regarding hard situations like war, the increasing cost of extraction and exploration of fossil fuels make governments move toward green and clear renewable energy (RE). As a result, we propose a novel multi-criteria decision-making (MCDM) method for RE location (REL) for the first time. This model suggests a Robust, Resilience MCDMwith Risk approach (RRMCDMR) for REL. We propose a risk approach by adding a risk function in MCDM. A robust convex approach is used to tackle the uncertainty of the model for the real world. We compare the RRMCDMR problem in a wind farm location in Iran with different risk coefficient functions. As defined, Khaf, Nehbandan, and Esfarayan are in locations one to three in all modes. We changed the normalized risk function and suggested two other risk functions that can help risk-averse and risk-neutral decision-makers. We varied the robust convex coefficient and considered that by increasing the robust convex coefficient, the alternative score increased.

Optimal shipping quantity, product pricing strategies and carbon emissions of online retailers under a new logistics mode

A new logistics mode has emerged in online retailing, which ships products before customers place orders online to reduce the waiting time for customers to receive them. The existing research on this logistics mode mainly focuses on the shipping quantity (i.e., the quantity of products to be shipped in advance from the order fulfillment center to the distribution center nearby customers before the order is placed online), while the product pricing problem and carbon emissions have not been studied comprehensively. Moreover, the risk attitudes of decision-makers have been ignored in the studies related to this new logistics mode. This paper builds an extended newsvendor model to explore the optimal joint decision problem of shipping quantity and product pricing under this new logistics mode and analyzes the carbon emissions of this new logistics mode compared with the traditional logistics mode. We consider decision-makers to be risk averse and take Conditional Value-at-Risk (CVaR) as the risk measure criterion. For both multiplicative and additive demand models, we obtain the closed-form solution of the optimal strategy. The differences between the optimal strategies of risk-averse and risk-neutral decision-makers and between the optimal strategies of this logistics mode and the traditional one have also been explored. Based on the optimal shipping quantity and product pricing strategies, we analyze the carbon emission variation of this logistics mode compared with the traditional one and provide sufficient conditions for reducing carbon emissions. Numerical experiments verify the theoretical conclusions and analyze the effect of some parameters on the optimal strategy, profit and carbon emission variation. The results show that online retailers should reduce product price in this new logistics mode compared with the traditional one. The risk-aversion degree slightly affects the optimal price but significantly affects the shipping quantity. Moreover, implementing this new logistics mode contributes to reducing carbon emissions compared with the traditional logistics mode in most cases. This study helps support online retailers in developing shipping quantity and product pricing strategies under this new logistics mode and helps the Environmental Protection Association to understand the carbon emissions under this new logistics mode so that relevant strategies can be developed.

Risk-averse supplier selection and order allocation in the centralized supply chains under disruption risks

This paper proposes a mixed-integer non-linear programming (MINLP) model for the integrated supplier selection and order allocation in a centralized supply chain considering the disruption risks and a risk-averse decision-maker. In order to capture a realistic scenario of considering the geographical characteristics of the suppliers, we assume that the suppliers belong to two regions: the buyer’s region (domestic suppliers) and outside of the buyer’s region (foreign suppliers). Considering this realistic feature, the supply chain might face two types of disruption risk: first, local disruption risks which might uniquely occur inside each supplier such as equipment breakdowns, and second, regional disruption risks that might occur in the region of the suppliers located in the same geographical region such as natural hazards. We formulate the problem considering a risk-neutral decision-maker as a benchmark, and then a risk-averse model is presented. In the latter case, we apply two types of risk assessment tools introduced in the finance literature to analyze the decision maker’s behavior: value-at-risk (VaR) and conditional value-at-risk (CVaR). We show that developed models are non-convex programming, and therefore, we apply the particle swarm optimization (PSO) algorithm as the solution approach. We also compare the developed PSO algorithm with the Genetic algorithm (GA) and the commercial GAMS solver to verify the efficiency of the solution method. The computational experiments indicate the impact of the decision maker’s attitude on the supplier selection and the order quantity.

Mixed financing strategies for capital-constrained retailer in the Chinese financial market

Retailers in supply chains usually deal with the problem of capital shortage by obtaining financing from the Chinese financial market. Examining the financing requirement of capital-constrained retailers, this paper studies the optimal decisions of the supplier and retailer in the supply chain, who are both risk-neutral decision-makers under wholesale price contracts. We assume that the retailer may obtain financing from a bank, the supplier and investors. Thus, the retailer can adopt two mixed financing modes: mixed financing of a bank and equity credit and mixed financing of trade and equity credit. We obtain equilibrium decisions under the two financing modes. By comparing the equilibrium results, we find that the mixed financing of trade and equity credit exhibits the only financing equilibrium. A Pareto interval of the wholesale price exists such that both the supplier and retailer can obtain higher profits with the mixed financing of trade and equity credit than the mixed financing of bank and equity credit. Finally, we present a numerical analysis to support our results.

Evaluation and designing reverse logistics for risk-neutral and risk-seeking decision makers

Designing appropriate supply chain would provide numerous valuable feedbacks for the whole chain, since using returned products instead of reproducing them, is a more appropriate response to the environmental concerns on the one hand which provides benefit and financial savings for the chains on the other hand. Therefore, this paper presents a three-objective function mathematical model to maximise financial savings and quantities of returned products to the chain and minimise total costs in terms of uncertainty and risk that derives from reverse logistics nature. Finally, the developed model was solved by Monte Carlo simulation and genetic algorithm along with proper risk measures for risk-neutral and risk-seeking decision makers. The results indicated financial savings are one of the best objective functions in order to show superiority of reverse logistics network. As another result, it was pointed out that profitability of the chain increases because of delivering return products before their scrap-life.

How to Play Fantasy Sports Strategically (and Win)

Daily fantasy sports (DFS) is a multibillion-dollar industry with millions of annual users and widespread appeal among sports fans across a broad range of popular sports. Building on recent work, we provide a coherent framework for constructing DFS portfolios where we explicitly model the behavior of other DFS players. We formulate an optimization problem that accurately describes the DFS problem for a risk-neutral decision maker in both double-up and top-heavy payoff settings. Our formulation maximizes the expected reward subject to feasibility constraints, and we relate this formulation to mean-variance optimization and the outperformance of stochastic benchmarks. Using this connection, we show how the problem can be reduced to the problem of solving a series of binary quadratic programs. We also propose an algorithm for solving the problem where the decision maker can submit multiple entries to the DFS contest. This algorithm is motivated by submodularity properties of the objective function and by some new results on parimutuel betting. One of the contributions of our work is the introduction of a Dirichlet-multinomial data-generating process for modeling opponents’ team selections, and we estimate the parameters of this model via Dirichlet regressions. A further benefit to modeling opponents’ team selections is that it enables us to estimate the value, in a DFS setting, of both insider trading and collusion. We demonstrate the value of our framework by applying it to DFS contests during the 2017 National Football League season. This paper was accepted by Baris Ata, stochastic models and simulation.

Optimizing surveillance strategies for early detection of invasive alien species

Surveillance programs to detect alien invasive pests seek to find them as soon as possible, but also to minimize the cost of damage from invasion. To examine the trade-offs between these objectives, we developed an economic model that allocates survey sites to minimize either the expected mitigation costs or the expected time until first detection of an invasive alien pest subject to a budget constraint on surveillance costs. We also examined strategies preferred by ambiguity-averse decision makers that minimize the expected and worst-case outcomes of each performance measure. We applied the model to the problem of detecting Asian longhorned beetle (Anoplophora glabripennis) in the Greater Toronto Area, Canada, one of the most harmful invasive alien insects in North America. When minimizing expected mitigation costs or expected time to detection, the trade-off between these survey objectives was small. Strategies that minimize the worst-case mitigation costs differed sharply and surveyed sites with high host densities using high sampling intensities whereas strategies that minimize the worst detection times surveyed sites across the entire area using low sampling intensities. Our results suggest that preferences for minimizing mitigation costs or time to detection are more consequential for ambiguity-averse managers than they are for risk-neutral decision-makers.

How to Play Fantasy Sports Strategically (and Win)

Daily Fantasy Sports (DFS) is a multi-billion dollar industry with millions of annual users and widespread appeal among sports fans across a broad range of popular sports. Building on the recent work of Hunter, Vielma and Zaman (2016), we provide a coherent framework for constructing DFS portfolios where we explicitly model the behavior of other DFS players. We formulate an optimization problem that accurately describes the DFS problem for a risk-neutral decision-maker in both double-up and top-heavy payoff settings. Our formulation maximizes the expected reward subject to feasibility constraints and we relate this formulation to mean-variance optimization and the out-performance of stochastic benchmarks. Using this connection, we show how the problem can be reduced to the problem of solving a series of binary quadratic programs. We also propose an algorithm for solving the problem where the decision-maker can submit multiple entries to the DFS contest. This algorithm is motivated by submodularity properties of the objective function and by some new results on parimutuel betting. One of the contributions of our work is the introduction of a Dirichlet-multinomial data generating process for modeling opponents' team selections and we estimate the parameters of this model via Dirichlet regressions. A further benefit to modeling opponents' team selections is that it enables us to estimate the value in a DFS setting of both insider trading and and collusion. We demonstrate the value of our framework by applying it to DFS contests during the 2017 NFL season.

Partially Observable Risk-Sensitive Markov Decision Processes

We consider the problem of minimizing a certainty equivalent of the total or discounted cost over a finite and an infinite time horizon that is generated by a partially observable Markov decision process (POMDP). In contrast to a risk-neutral decision maker, this optimization criterion takes the variability of the cost into account. It contains as a special case the classical risk-sensitive optimization criterion with an exponential utility. We show that this optimization problem can be solved by embedding the problem into a completely observable Markov decision process with extended state space and give conditions under which an optimal policy exists. The state space has to be extended by the joint conditional distribution of current unobserved state and accumulated cost. In case of an exponential utility, the problem simplifies considerably and we rediscover what in previous literature has been named information state. However, since we do not use any change of measure techniques here, our approach is simpler. A simple example, namely, a risk-sensitive Bayesian house selling problem, is considered to illustrate our results.

Moving beyond the cost–loss ratio: economic assessment of streamflow forecasts for a risk-averse decision maker

Abstract. A large effort has been made over the past 10 years to promote the operational use of probabilistic or ensemble streamflow forecasts. Numerous studies have shown that ensemble forecasts are of higher quality than deterministic ones. Many studies also conclude that decisions based on ensemble rather than deterministic forecasts lead to better decisions in the context of flood mitigation. Hence, it is believed that ensemble forecasts possess a greater economic and social value for both decision makers and the general population. However, the vast majority of, if not all, existing hydro-economic studies rely on a cost–loss ratio framework that assumes a risk-neutral decision maker. To overcome this important flaw, this study borrows from economics and evaluates the economic value of early warning flood systems using the well-known Constant Absolute Risk Aversion (CARA) utility function, which explicitly accounts for the level of risk aversion of the decision maker. This new framework allows for the full exploitation of the information related to a forecasts' uncertainty, making it especially suited for the economic assessment of ensemble or probabilistic forecasts. Rather than comparing deterministic and ensemble forecasts, this study focuses on comparing different types of ensemble forecasts. There are multiple ways of assessing and representing forecast uncertainty. Consequently, there exist many different means of building an ensemble forecasting system for future streamflow. One such possibility is to dress deterministic forecasts using the statistics of past error forecasts. Such dressing methods are popular among operational agencies because of their simplicity and intuitiveness. Another approach is the use of ensemble meteorological forecasts for precipitation and temperature, which are then provided as inputs to one or many hydrological model(s). In this study, three concurrent ensemble streamflow forecasting systems are compared: simple statistically dressed deterministic forecasts, forecasts based on meteorological ensembles, and a variant of the latter that also includes an estimation of state variable uncertainty. This comparison takes place for the Montmorency River, a small flood-prone watershed in southern central Quebec, Canada. The assessment of forecasts is performed for lead times of 1 to 5 days, both in terms of forecasts' quality (relative to the corresponding record of observations) and in terms of economic value, using the new proposed framework based on the CARA utility function. It is found that the economic value of a forecast for a risk-averse decision maker is closely linked to the forecast reliability in predicting the upper tail of the streamflow distribution. Hence, post-processing forecasts to avoid over-forecasting could help improve both the quality and the value of forecasts.

Determining the appropriate timing of the next forest inventory: incorporating forest owner risk preferences and the uncertainty of forest data quality

The timing to conduct new forest inventories should be based on the requirements of the decision maker. Importance should be placed on the objectives of the decision maker and his/her risk preferences related to those objectives. The appropriate use of pertinent and available information is paramount in any decision-making process. Within forestry, a new forest inventory is typically conducted prior to creating a forest management plan. The acquisition of new forest inventory data is justified by the simple statement of “good decisions require good data.” By integrating potential risk preferences, we examine the specific needs to collect new forest information. Through a two-stage stochastic programming with recourse model, we evaluate the specific timing to conduct a holding level forest inventory. A Monte Carlo simulation was used to integrate both inventory and growth model errors, resulting in a large number of potential scenarios process to be used as data for the stochastic program. To allow for recourse, an algorithm to sort the simulations to represent possible updated forest inventories, using the same data was developed. Risk neutral decision makers should delay obtaining new forest information when compared to risk averse decision makers. New inventory data may only need to be collected rather infrequently; however, the exact timing depends on the forest owner’s objectives and risk preferences.

An economic model to evaluate information security investment of risk-taking small and medium enterprises

This paper analyzes information security investment decisions made by risk taking small and medium enterprises (SMEs) using the expected utility approach. It then compares these decisions to ones made by a risk neutral firm. We find that risk takers are inclined to prioritize an information set's vulnerability over its value when making investment decisions. We also find that a risk taking firm may invest a larger amount in protecting a set than the risk neutral firm when the effectiveness of the investment in lowering breach probability is low. Finally, we show that for a group of information sets of equal value and varying vulnerabilities, the risk neutral decision maker will diversify security investment to a greater extent than the risk taker. As a result, the risk taker will invest a larger amount than the risk neutral firm would when protecting the high risk sets in the group. The results provide guidance to information security vendors when tailoring products to suit small businesses.

Supplier selection and order allocation under disruption risk

The supplier’s risk is nowadays one of the important topics in the supply chain management. This paper studies the problem of the supplier’s selection and order allocation in a make-to-order environment in the presence of disruption risk supplier. Two mixed integer programs are developed. The first considers a risk neutral decision-maker who maximizes the expected profit, whereas the second regards a risk-averse decision-maker someone who minimizes the expected operational loss. The results demonstrate that the expected profit and the operational loss evolve in the same way. An increase of the expected profit will also increase the expected loss, which, in turn, reduces the profit. Our goal is to produce the evolution curve of these two indicators and provide the decision-maker with visual aid to choose solution corresponding to his sensitivity to risk

An utility-based decision support sustainability model in slow steaming maritime operations

This paper analyses slow steaming sustainability initiatives and generalizes the traditional discrete cost-based decision support model into novel continuous utility-based models. Two models based on logarithmic and linear utility functions are developed for risk-averse and risk-neutral decision makers respectively. The models, considering fuel consumption, carbon emission, and on time delivery, are applied to a Trans-pacific trade service route. A sensitivity analysis is conducted on parameters of sailing distance, expected transit time, quantity, and emission policies. The model contributes to ship liners on the optimal speed decisions in continuous utility-based slow steaming operations.

Engineering Decisions under Risk Averseness

AbstractEngineering decisions are invariably made under substantial uncertainty about current and future system cost and response, including cost and response associated with low-probability, high-consequence events. A risk-neutral decision maker would rely on expected values when comparing designs, while a risk-averse decision maker might adopt nonlinear utility functions or failure probability criteria. The paper shows that these models for making decisions are related to a framework of risk measures that includes many possibilities. The authors describe how risk measures provide an expanded set of models for handling risk-averse decision makers. General recommendations for selecting risk measures lead to decision models for risk-averse decision making that comprehensively represent risks in engineering systems, avoid paradoxes, and accrue substantial benefits in subsequent risk, reliability, and cost optimization. The paper provides an overview of the framework of decision making based on risk measures.

Optimal Pricing and Order-Up-To S Inventory Policy with Expected Utility of the Present Value Criterion

The article determines pricing and order-up-to level S inventory decisions over an infinite planning horizon from the point of view of a risk-averse decision maker. The demand is assumed to be stochastic but influenced by the selling price which is a decision variable. Shortages are allowed and backordered partially. We calculate the present value of the cash flow over the entire planning horizon and incorporate the notion of risk aversion into the model using a concave utility function. We numerically demonstrate the model and investigate the impact of different model-parameters on the optimal decisions. It is observed that the optimal selling price for a risk-averse decision maker is not less than the optimal selling price of a risk-neutral decision maker while the optimal order level for the risk-averse decision maker is always less than that of the risk-neutral decision maker.