Risk Aversion Parameter Research Articles

A generalized behavioral-based goal programming approach for decision-making under imprecision

The body of literature on goal programming (GP) approaches in modeling preferences and the satisfaction philosophy in multi-objective programming (MOP) decision-making processes is extensive. However, there has been little focus on how preferences change in relation to the decision-maker's (DM) behavior within this satisfaction philosophy, particularly in situations involving risk. To address this challenge, we propose introducing a behavior-type utility function into the GP model using the concept of a behavior function. This idea offers an innovative perspective for modeling DM's behavioral preferences in the imprecise GP approach by integrating a risk-aversion parameter specific to each objective. We then formulate a generalized behavioral-based GP approach for decision-making based on this new behavior-type utility function. To validate our proposed approach, we present an illustrative example of project selection in health service institutions, followed by a sensitivity analysis and comparisons with other approaches. The results demonstrate that DM's behavioral preferences significantly impact the decision-making process, and the proposed model provides more reasonable and convenient decisions for DMs with varying degrees of risk aversion.

Properties of risk aversion estimated from portfolio weights

While risk tolerance is often elicited using questionnaire-based instruments, in this paper, we evaluate the merits of an inversion-based technique, wherein risk aversion parameters are inferred from an individual’s portfolio holdings and a sequence of realized returns. We obtain expressions for the finite sample and asymptotic variance of the estimated risk aversion parameter under the inversion approach with a single risky asset, demonstrating that confidence intervals for parameter estimates are relatively wide. Extending the analysis, we show that inferring risk aversion from multiple risky assets does not typically serve to reduce the estimated parameter variance, but rather propagates estimation error.

A novel behavioral penalty function for interval goal programming with post-optimality analysis

Goal programming (GP) is a multi-objective extension of linear programming. Interval GP (IGP) is one of the earliest methods to expand the range of preferred structures in GP. The decision maker’s (DM’s) utility or preference in IGP is investigated by incorporating a widening range of underlying utility functions, commonly known as penalty functions. The basic idea of these functions is that undesirable deviations from the target levels of the goals are penalized regarding a constant or variable penalty value. The main concern with introducing the penalty functions is providing a wide range of a priori preference structures. Yet, the evaluation of how undesirable deviations are penalized based on DM’s behavioral preferences is not sufficiently addressed in the penalty function types developed in the GP literature. In real-world scenarios involving risk, the achievement levels of decision-making attributes are typically associated with the behavior of the DM. In such scenarios, the DM’s unavoidable attitude toward risk should be integrated into the decision-making process. We introduce the concept of behavioral penalty functions into the IGP approach, incorporating a risk aversion parameter tailored to the nature of each attribute to address this gap. This concept offers an innovative framework for capturing the preferences of the DMs and their various attitudes toward risk within the IGP approach. In this paper, we first introduce the concept of behavioral penalty functions. Next, we develop a behavioral utility-based IGP model. Finally, we present a portfolio selection case study to demonstrate the applicability and efficacy of the proposed procedure, followed by a post-optimality analysis and comparisons with other GP approaches.

Robust Portfolio Mean-Variance Optimization for Capital Allocation in Stock Investment Using the Genetic Algorithm: A Systematic Literature Review

Traditional mean-variance (MV) models, considered effective in stable conditions, often prove inadequate in uncertain market scenarios. Therefore, there is a need for more robust and better portfolio optimization methods to handle the fluctuations and uncertainties in asset returns and covariances. This study aims to perform a Systematic Literature Review (SLR) on robust portfolio mean-variance (RPMV) in stock investment utilizing genetic algorithms (GAs). The SLR covered studies from 1995 to 2024, allowing a thorough analysis of the evolution and effectiveness of robust portfolio optimization methods over time. The method used to conduct the SLR followed the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines. The result of the SLR presented a novel strategy to combine robust optimization methods and a GA in order to enhance RPMV. The uncertainty parameters, cardinality constraints, optimization constraints, risk-aversion parameters, robust covariance estimators, relative and absolute robustness, and parameters adopted were unable to develop portfolios capable of maintaining performance despite market uncertainties. This led to the inclusion of GAs to solve the complex optimization problems associated with RPMV efficiently, as well as fine-tuning parameters to improve solution accuracy. In three papers, the empirical validation of the results was conducted using historical data from different global capital markets such as Hang Seng (Hong Kong), Data Analysis Expressions (DAX) 100 (Germany), the Financial Times Stock Exchange (FTSE) 100 (U.K.), S&P 100 (USA), Nikkei 225 (Japan), and the Indonesia Stock Exchange (IDX), and the results showed that the RPMV model optimized with a GA was more stable and provided higher returns compared with traditional MV models. Furthermore, the proposed method effectively mitigated market uncertainties, making it a valuable tool for investors aiming to optimize portfolios under uncertain conditions. The implications of this study relate to handling uncertainty in asset returns, dynamic portfolio parameters, and the effectiveness of GAs in solving portfolio optimization problems under uncertainty, providing near-optimal solutions with relatively lower computational time.

Ship coping strategies for hurricane-induced port disruptions

PurposeDisruptions at ports may destroy the planned ship schedules profoundly, which is an imperative operation problem that shipping companies need to overcome. This paper attempts to help shipping companies cope with port disruptions through recovery scheduling.Design/methodology/approachThis paper studies the ship coping strategies for the port disruptions caused by severe weather. A novel mixed-integer nonlinear programming model is proposed to solve the ship schedule recovery problem (SSRP). A distributionally robust mean conditional value-at-risk (CVaR) optimization model was constructed to handle the SSRP with port disruption uncertainties, for which we derive tractable counterparts under the polyhedral ambiguity sets.FindingsThe results show that the size of ambiguity set, confidence level and risk-aversion parameter can significantly affect the optimal values, decision-makers should choose a reasonable parameter combination. Besides, sailing speed adjustment and handling rate adjustment are effective strategies in SSRP but may not be sufficient to recover the schedule; therefore, port skipping and swapping are necessary when multiple or longer disruptions occur at ports.Originality/valueSince the port disruption is difficult to forecast, we attempt to take the uncertainties into account to achieve more meaningful results. To the best of our knowledge, there is barely a research study focusing on the uncertain port disruptions in the SSRP. Moreover, this is the first paper that applies distributionally robust optimization (DRO) to deal with uncertain port disruptions through the equivalent counterpart of DRO with polyhedral ambiguity set, in which a robust mean-CVaR optimization formulation is adopted as the objective function for a trade-off between the expected total costs and the risk.

Newsvendor model for a dyadic supply chain with push-pull strategy under shareholding and risk aversion

This paper investigates the optimization and coordination problem in the framework of classic push and pull newsvendor models under shareholding and CVaR criterion. A decentralized supply chain consisting of upstream supplier and the downstream manufacturer is considered. Firstly, taking the risk aversion into account, the optimal decision-makings are investigated under shareholding in push, pull supply chain respectively. By comparison it is found that the optimal order or production quantity depends on the degree of member’s risk aversion and shareholding ratio. Furthermore, the combined contracts are designed to coordinate the supply chain and optimal coordination parameters are obtained. Besides, the impacts of risk-averse preference and the shareholding fraction on supply chain performance are also investigated. The results indicate that in push supply chain the optimal ordering increases in the risk-averse parameter of the downstream manufacturer and the percentage of shares held by the upstream supplier in the downstream manufacturer. However, the optimal wholesale price makes the opposite change. In pull supply chain, the optimal production quantity is independent of the shareholding fraction and decreases with regards to the supplier’s risk aversion. Lastly, some numerical examples are given to illustrate the theoretical results and some suggestions to supply chain management are also provided.

A dynamic game approach for optimal consumption, investment and life insurance problem

AbstractIn this paper, we consider a multi-agent portfolio optimization model with life insurance for two players with random lifetime under a dynamic game approach. Each player is a price-taker and invests in the market to maximize her own utility for consumption and bequest. The market is complete and consists of n different assets, of which $$n-1$$ n - 1 are risky with prices driven by Geometric Brownian motion, while one is risk-free. We analyze both the non-cooperative and cooperative scenarios, and by considering the family of CRRA utility functions, we determine the closed-form expressions of the optimal consumption, investment, and life insurance for both players. A sensitivity analysis is provided both to illustrate the impact of the biometric and risk aversion parameters on the optimal controls and to compare the non-cooperative strategies with the cooperative ones. As a result, we suggest that cooperation favors the consumption optimality, while non-cooperation promotes the coverage of the risk of death.

The Impact of Commitment on Pending Home Sales in Entrapping Situations

This paper examines the decision-making processes of home buyers during the Global Financial Crisis, with a specific focus on passive coping mechanisms and the role of risk aversion. The study investigates how risk aversion influences the behavior of home buyers and highlights the disparities between high-income and low-income buyers. The findings reveal that high-income home buyers exhibit a risk aversion parameter that ranges from 1.74 to 1.99, while low-income home buyers have a parameter that ranges from 0.60 to 0.62, thus indicating different levels of risk tolerance and decision-making patterns among the income groups. These findings suggest that low-income home buyers are more likely to endure unfavorable situations or avoid making changes in periods of declining house prices than high-income home buyers. This behavior aligns with the concept of passive coping, where low-income home buyers choose to endure unfavorable situations rather than making changes because they fear the negative outcomes that may arise from taking a different course of action. They might worry that if they abandon the contract, they will miss out on the opportunity to own a home, live in a desirable neighborhood, or secure a specific property. This fear of potential losses leads them to choose passive coping, where they endure the current situation rather than making changes that could involve risks or uncertainties.

A risk-averse sustainable perishable food supply chain considering production and delivery times with real-world application.

In recent years, a relatively novel paradigm known as sustainable development has been introduced in response to concerns regarding the adverse impact of industrial activities on the environment and society. Managers in the food sector have been attempting to incorporate the principle of sustainable development in their supply chains owing to the paramount importance of social and environmental considerations in creating a competitive advantage for food products. To this end, we propose a multi-objective linear mathematical model considering the three dimensions of sustainability, i.e. economic, environmental, and social, to design a sustainable food supply chain. Given today's volatile business environment, we employ a robust optimization model by incorporating Conditional Value-at-Risk into the configuration of two-stage stochastic programming to tackle uncertainty and take up a risk-averse strategy in supply chain design. The model aims to identify the optimal production and delivery times of the products, investigate the effects of their perishability characteristic on inventory decisions, and assess the financial and environmental advantages of transportation decisions to improve the sustainability of logistics operations. A novel version of fuzzy goal programming approach is applied to solve the proposed model. Next, the applicability of the proposed model and its solution method is verified based on computational experiments on a real-world case study of a processed food company. Lastly, conflicts between the sustainability aspects are examined, and several sensitivity analyses on risk-aversion parameters are performed to provide managerial insights for industry executives seeking to optimize their network concerning sustainability issues and well-performance under worst-case scenarios.

The Impact of Commitment on Pending Home Sales in Entrapping Situations

This paper examines the decision-making processes of home buyers during the Global Financial Crisis, with a specific focus on passive coping mechanisms and the role of risk aversion. The study investigates how risk aversion influences the behavior of home buyers and highlights the disparities between high-income and low-income buyers. The findings reveal that high-income home buyers exhibit a risk aversion parameter that ranges from 1.74 to 1.99, while low-income home buyers have a parameter that ranges from 0.60 to 0.62, thus indicating different levels of risk tolerance and decision-making patterns among the income groups. These findings suggest that low-income home buyers are more likely to endure unfavorable situations or avoid making changes in periods of declining house prices than high-income home buyers. This behavior aligns with the concept of passive coping, where low-income home buyers choose to endure unfavorable situations rather than making changes because they fear the negative outcomes that may arise from taking a different course of action. They might worry that if they abandon the contract, they will miss out on the opportunity to own a home, live in a desirable neighborhood, or secure a specific property. This fear of potential losses leads them to choose passive coping, where they endure the current situation rather than making changes that could involve risks or uncertainties.

The impact of ambiguity on dynamic portfolio selection in the epsilon-contaminated binomial market model

We consider dynamic portfolio selection under ambiguity in the classical multi-period binomial market model. Ambiguity is incorporated in the real-world probability measure through an epsilon-contamination, that gives rise to a completely monotone capacity conveying a pessimistic investor’s ambiguous beliefs. The dynamic portfolio selection problem is formulated as a Choquet expected utility maximization problem on the final wealth. Then, the optimal final wealth is proved to be a function of the final stock price: this allows a dimension reduction of the problem, switching from an exponential to a linear size with respect to the number of periods. Finally, an explicit characterization of the optimal final wealth is given in the case of a constant relative risk aversion utility function and the interaction between the ambiguity and the relative risk aversion parameters is investigated.

A multi-stage decision framework for managing hazardous waste logistics with random release dates

This research develops a multi-stage decision framework for a three-tier collection network for hazardous waste considering random release dates. Applying a cost-based clustering approach, the first stage decisions involve locating the transfer stations and allocating generation nodes to the chosen facilities. The corresponding results, along with a subjective risk-aversion concept and estimated release dates, are utilized to generate an a priori collection plan, which can be further revised once the actual release dates are realized. We performed sensitivity analyses on important model elements, including the subjective risk-aversion parameter and vehicle capacity for collection tours. Our findings indicate that depending on the subjective perspective of the collector, deviations from the original scheduled plan can be a positive or negative phenomenon. For an optimistic decision-maker, adaption to the realized deviations necessitates accepting additional total risk. On the other hand, a pessimistic decision-maker is more likely to benefit from deviations. The findings can provide relevant authorities with practical and realistic strategic and operational decisions.

Modeling the optimal sizing problem of the biogas-based electrical generator in a livestock farm considering a gas storage tank and the anaerobic digester process under the uncertainty of cow dung

Cow dung is the main source of producing methane, as one of the greenhouse gases. To decrease this pollution, cow dung can be transformed into biogas, and consequently, the produced biogas can be used as a fuel for electrical generators. This problem is addressed in the so far researches without proposing the appropriate mathematical models. In this paper, the optimal sizing problem of the biogas-based generators (BGs) is formulated for a livestock farm by modeling the anaerobic digester process and the gas storage tank. To protect the system operator's decisions against the uncertainty of the cow dung, the proposed model is reformulated as a risk-based model using the information gap decision theory. The obtained capacity of the BG and the storage tank for a livestock farm with 2000 cows are 433.24 kW and 628.056 m3, respectively. Also, the designed system prevents releasing approximately 522-ton pollution. The results show the appropriate performance of the system operator to use the produced gas to be directly sent to the BG and/or to charge the storage tank. The results show that with increasing the risk-aversion parameter, the capacity of the BG and the storage tank decrease which leads to decreasing the total profit.

Optimal energy portfolio allocation method for regulable hydropower plants considering the impact of new energy generation

With the growing penetration of new energy sources, the impact of new energy generation on the income of the energy portfolio is becoming more significant. This paper proposes a risk measurement method based on the Conditional Value-at-Risk (CVaR) approach to measure the income risk from new energy generation on the energy portfolio. The superiority is proved by comparing it with the method only considering spot price fluctuations. Then, we constructed an energy allocation model of the hydropower plant to maximize the combined income-risk utility. In solving the optimal allocation of the energy portfolio, the effects of inflow and water level on the risk aversion parameters of the hydropower plant are considered. The results and comparison show that the proposed risk measurement method increases the income of the energy portfolio by 12%, and the proposed risk aversion parameter’s adjustment strategy can increase the income of the energy portfolio by 5.8% and reduces the CVaR value by 14.5%. Moreover, the method that considers the income risk from new energy generation can provide favorable conditions for improved new energy accommodation and safe operation of the system.

Reliability of Decision-Making and Reinforcement Learning Computational Parameters.

Computational models can offer mechanistic insight into cognition and therefore have the potential to transform our understanding of psychiatric disorders and their treatment. For translational efforts to be successful, it is imperative that computational measures capture individual characteristics reliably. Here we examine the reliability of reinforcement learning and economic models derived from two commonly used tasks. Healthy individuals (N = 50) completed a restless four-armed bandit and a calibrated gambling task twice, two weeks apart. Reward and punishment learning rates from the reinforcement learning model showed good reliability and reward and punishment sensitivity from the same model had fair reliability; while risk aversion and loss aversion parameters from a prospect theory model exhibited good and excellent reliability, respectively. Both models were further able to predict future behaviour above chance within individuals. This prediction was better when based on participants' own model parameters than other participants' parameter estimates. These results suggest that reinforcement learning, and particularly prospect theory parameters, as derived from a restless four-armed bandit and a calibrated gambling task, can be measured reliably to assess learning and decision-making mechanisms. Overall, these findings indicate the translational potential of clinically-relevant computational parameters for precision psychiatry.

A reinforcement learning approach to improve the performance of the Avellaneda-Stoikov market-making algorithm.

Market making is a high-frequency trading problem for which solutions based on reinforcement learning (RL) are being explored increasingly. This paper presents an approach to market making using deep reinforcement learning, with the novelty that, rather than to set the bid and ask prices directly, the neural network output is used to tweak the risk aversion parameter and the output of the Avellaneda-Stoikov procedure to obtain bid and ask prices that minimise inventory risk. Two further contributions are, first, that the initial parameters for the Avellaneda-Stoikov equations are optimised with a genetic algorithm, which parameters are also used to create a baseline Avellaneda-Stoikov agent (Gen-AS); and second, that state-defining features forming the RL agent's neural network input are selected based on their relative importance by means of a random forest. Two variants of the deep RL model (Alpha-AS-1 and Alpha-AS-2) were backtested on real data (L2 tick data from 30 days of bitcoin-dollar pair trading) alongside the Gen-AS model and two other baselines. The performance of the five models was recorded through four indicators (the Sharpe, Sortino and P&L-to-MAP ratios, and the maximum drawdown). Gen-AS outperformed the two other baseline models on all indicators, and in turn the two Alpha-AS models substantially outperformed Gen-AS on Sharpe, Sortino and P&L-to-MAP. Localised excessive risk-taking by the Alpha-AS models, as reflected in a few heavy dropdowns, is a source of concern for which possible solutions are discussed.

A capacitated lot-sizing problem in the industrial fashion sector under uncertainty: a conditional value-at-risk framework

In this study, we present a multi-product, multi-period inventory control problem under uncertainty in product demands that emerges in the fashion industry. A two-stage stochastic model is proposed to design a planning strategy where the total cost incurred by purchase orders, inventory and shortage is minimised. We incorporate the Conditional Value at Risk (CVaR) within the formulation to address exogenous uncertainty. An industrial case study involving a Mexican fashion retail company was considered to assess the performance of the two-stage stochastic model. Scenarios were considered using historical data provided by the company. A sensitivity analysis was also conducted on risk-aversion parameters to assess how the values of these parameters affect the behaviour of the proposed formulation. The results show that the proposed two-stage stochastic formulation is an efficient and practical approach to handle exogenous uncertainty in industrial-scale capacitated lot-sizing problems.

RELIABLE PLANNING OF HINTERLAND-PORT FREIGHT NETWORK AGAINST TRANSFER DISRUPTION RISKS

Many previous cases have shown that port operations are susceptible to disruptive events. This paper proposes 2-stage Stochastic Programming (SP) for port users to reliably plan the hinterland-port intermodal freight network with consideration of risk aversion in cost. Probabilistic disruptions of intermodal terminals are considered as scenario-specific. In the 1st stage, intermodal paths are selected to obtain proper network capacities. In the 2nd stage, cargo flows are assigned for each disruption scenario on the planed network. The 2-stage model is firstly formulated in a risk-neutral environment to achieve the minimum expectation of total cost. Then, the Mean-Risk (MR) framework is adopted by incorporating a risk measure tool called Conditional Value-at-Risk (CVaR) into the expectation model, so as to reduce the cost of worst-case disruption scenarios. Benders’ Decomposition (BD) is introduced to efficiently solve the exponential many problem. Some numerical experiments are performed under different risk aversion parameters. With this study, network planners can decide network capacities with reasonable redundancies to improve the freight reliability in a cost-effective way. The proposed method provides a simple approach for the planners to quantify their risk appetites in cost and to impose them in the planning process, hence to trade-off the Expected Cost (EC) and the worst-case cost.

Insurance with heterogeneous preferences

This paper studies an optimal insurance problem with finitely many potential policyholders. A monopolistic, risk-neutral insurer applies linear pricing, and cannot discriminate in the insurance premium rate. The individuals are endowed with exponential expected utility preferences, and there is heterogeneity in the risk-aversion parameters. We study two models. In the first model the individuals can self-select their insurance coverage given the market premium rate. We find that partial or no insurance is generally optimal, and the premium optimization can be reduced to a piecewise concave problem. In the second model, the insurer offers only one insurance contract and individuals can either buy it or not. We show that it is optimal for the insurer to offer a full insurance contract. The premium optimization problem is reduced to a discrete problem, where the premium is an indifference premium of one individual in the market. Since the risk-aversion parameters of individuals are generally unobserved, we also present a simulation-based framework in which we simulate the risk-aversion parameters of the individuals. We show that the model with finitely many policyholders converges to the model with a continuum of potential policyholders when the number of potential individuals increases.

Preferences after pan(dem)ics: Time and risk in the shadow of COVID-19

AbstractThis paper uses the COVID-19 health crisis to study how individual preferences respond to generalized traumatic events. We review previous literature on natural and man-made disasters. Using incentive-compatible tasks, we simultaneously estimate risk and ambiguity aversion, time discounting, present bias, and prudence parameters before, during, and after the COVID-19 lockdown in France. We find patience, risk aversion, and ambiguity aversion fell during lockdown, then gradually returned toward their initial levels 4 months later. These results have implications for health and economic policies, and deepen our understanding of the responses – and resilience – of economic preferences to traumatic events.