Mean-variance Utility Research Articles

Decision-making in closed-loop supply chains: Effects of government subsidies and risk aversion

Closed-loop supply chains (CLSCs) play a crucial role in promoting sustainable resource management, yet their implementation faces challenges in balancing economic viability with environmental goals. While existing research has explored various aspects of CLSC operations, the interplay between government subsidies and risk-averse behavior of supply chain members remains understudied, particularly in systems involving third-party recyclers. This gap hinders the development of effective policies and management strategies for sustainable CLSCs. Herein, we employ a Stackelberg game-theoretic model to investigate decision-making processes in CLSCs under four distinct subsidy scenarios, incorporating risk aversion through mean-variance utility functions. Our results reveal that subsidy effectiveness significantly depends on remanufacturing costs and risk attitudes of supply chain participants. When remanufacturing costs are high, subsidizing third-party recyclers yields superior environmental and economic outcomes, whereas manufacturer subsidies prove more effective when these costs are low. Moreover, we identify critical thresholds in subsidy levels and risk aversion that alter decision-making patterns. These findings provide a framework for designing targeted subsidy policies and risk management strategies in CLSCs, advancing the field of sustainable supply chain management by offering nuanced insights into the complex dynamics between government interventions, risk preferences, and CLSC performance.

Optimal employment decisions in the hospitality sector under uncertain productivity loss due to catastrophe: A mean-variance utility approach

How do exogenous disruptions such as natural disasters affect employment and labour productivity in the hospitality sector? This article addresses this crucial issue by proposing a two-moment (i.e., mean-variance) decision model to determine the pattern of productivity and employment losses in this sector. In our model, a representative hotel owner selects the optimal employment level based on the risk-taking orientation of the manager. During a catastrophe, a high operational fixed investment cost causes optimal employment decisions for a hotel owner to become an endogenous choice variable. Our proposed model and a calibration exercise predict that, on average, as operational uncertainty increases, expected profits decrease substantially, causing managers to terminate employees. Government intervention in the form of a lumpsum grant can be beneficial, but the level of the grant should be contingent on the risk preference of the hotel management. For instance, restoring complete employment with a substantial lump-sum aid may take longer. We discuss the implications of our findings for hospitality sector research and tourism industry professionals.

Beyond financial wealth: The experienced utility of collectibles

We argue that the utility of specific assets, in our case collectibles, is not only derived from the financial outcome, but also from the conditions that prevail until a financial outcome may be realized. Therefore, we derive a multi-attribute utility function that measures financial returns — using a mean-variance utility function — on the one hand, and non-financial returns — using an experienced utility function — on the other. We then reveal the trade-off between financial and non-financial utility by analyzing 363 owners of collectibles. We divide the owners into the group of collectors and the group of investors, based on their self-reported motivation. Our results suggest that collectors receive almost no utility from financial returns, but rather from experience. The opposite is the case for investors. Our findings help to explain the reported financial underperformance of collectibles and suggest to adjust existing models of utility.

Robust portfolio selection with smart return prediction

Return prediction and portfolio decision are closely connected steps in forming optimal portfolios. However, existing studies often separate return prediction from portfolio decisions or overlook the high sensitivity of optimal portfolios to estimated returns, leading to poor out-of-sample performance. To address these two issues simultaneously, this paper proposes a robust portfolio framework that optimizes parameters in return prediction by maximizing robust mean–variance utility. The proposed framework effectively combines return prediction and portfolio decisions while mitigating the uncertainty in return prediction. Empirical analysis on S&P500 constituents demonstrates that, compared to the benchmarks, the proposed framework achieves lower risk and higher risk-adjusted returns, originating from more stable weight estimation and diversified portfolios. Further, we uncover that the market friction characteristics considerably contribute to the proposed strategies’ performance. Our results suggest that integrating return prediction with the robust mean–variance models can significantly improve portfolio performance.

Volatility prediction for the energy sector with economic determinants: Evidence from a hybrid model

Given close ties between energies and economic growth and evidence in the literature that fundamental information helps improve the pricing efficiency of energy products, in this study we examine volatility prediction for the U.S. energy sector considering the impact of economic variables. In particular, we develop a hybrid model that combines the GARCH-MIDAS model and LSTM neural network. This particular specification is motivated by the need to simultaneously take a large number of economic predictors into account and allow a flexible volatility component structure with potential nonlinear relation among economic determinants. Based on the sample period from January 1991 to September 2022, our empirical results show that the hybrid model generates statistically more precise volatility forecasts out of sample than a number of alternative models, and this is robust during the energy market turmoil brought by the onset of the COVID-19 pandemic and the Russian–Ukrainian clash. Finally, volatility forecasts from the hybrid model allow mean–variance utility investors to achieve higher economic value.

Stochastic differential investment and reinsurance game between an insurer and a reinsurer under thinning dependence structure

This paper investigates a non-zero-sum stochastic differential investment and reinsurance game between an insurer and a reinsurer. It is assumed that the insurer can purchase proportional reinsurance and the claim businesses between the insurer and the reinsurer are correlated through thinning dependence structure. Besides, both the insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset, in which the two risky assets are supposed to be correlated. The objective of each is to maximize the mean–variance utility of the difference between its terminal wealth and that of its cooperator. By solving the extended Hamilton–Jacobi–Bellman systems within the game theoretic framework, explicit expressions of the optimal time-consistent strategies and value functions of the insurer and the reinsurer are derived, and some comparison results with and without game are obtained as well. Finally, several sensitivity analyses and numerical examples are presented to illustrate the effects of market parameters on the optimal strategies as well as the economic interpretation behind.

A DC Plan with Return Clause and Administrative Charges under Heston Volatility and Weibull Model under Mean Variance Utility

A DC Plan with Return Clause and Administrative Charges under Heston Volatility and Weibull Model under Mean Variance Utility

Forecasting Chinese stock market volatility with option-implied risk aversion: Evidence from extended realized EGARCH-MIDAS approach

This paper investigates the role of option-implied risk aversion (IRA) in forecasting the Chinese stock market volatility. We derive the IRA from the SSE 50ETF option prices using behavioral pricing kernel theory. We extend the realized EGARCH-MIDAS (REGARCH-MIDAS) model to incorporate the IRA. Furthermore, we propose the REGARCH-MIDAS-IRA-ES model accounting for the extreme IRA information to model and forecast the Chinese stock market volatility. Empirical results based on the extended REGARCH-MIDAS models show that the IRA has a significantly positive impact on the long-term volatility of Chinese stock market, and the extremely positive IRA has a greater impact on the long-term volatility compared to the extremely negative and normal IRA. Moreover, the IRA possesses predictive value for the Chinese stock market volatility. In particular, we observe that the extreme IRA can provide more valuable information to forecast the Chinese stock market volatility. Our proposed REGARCH-MIDAS-IRA-ES model outperforms a variety of competing models in terms of out-of-sample volatility forecast. We confirm that the superior forecasting performance of the model is robust to different out-of-sample evaluation approach, different out-of-sample forecast windows, different MIDAS lags and different volatility states. Finally, a volatility-timing strategy demonstrates that incorporating the IRA, and in particular the extreme IRA, leads to economic gains for a mean–variance utility investor.

An Equilibrium Strategy for Target Benefit Pension Plans with a Longevity Trend and Partial Information

This paper considers the problem of portfolio selection and adjustment for target benefit plans (TBP) with longevity trends and partial information. The longevity trends are modeled by a time-varying force function. The financial market consists of risk-free assets and stocks, in which the return rate of stocks is a stochastic process and cannot be completely observed. This paper adopts the mean-variance utility model as an optimization criterion. The aim is to maximize the terminal value of the pension fund and the excess pension benefit after the participant’s retirement. The optimization equations are developed in game theory to obtain explicit solutions for the equilibrium strategies. Finally, the influence of the longevity trend on the internal structure of the pension system and the sensitivity of the equilibrium strategies to the related parameters are explored by numerical analysis. The conclusion shows that this model’s results can provide stable and adequate retirement benefits for participants.

A comprehensive functional form of the optimal harvest control rule for multiple fishery management objectives

For many of the world's fisheries, harvest control rules (HCRs) are the main tools for supporting decision-making. We previously clarified the optimal shape of the HCR to achieve multiple fisheries management objectives (maximising average catch, reducing variation in yields, and avoiding stock collapse) and ensure robustness to estimation errors in biomass by numerically estimating the optimal values of the 21 biological reference points (BRPs) comprised in the HCR. However, for actual management, a simple but comprehensive functional form to emulate the optimal HCR is desirable, as numerical HCR optimisation with many BRPs is time-consuming. Here, we introduced three objective utility functions ( U1– U3) representing HCR performance for composite management objectives: mean–variance utility functions, where the performance indicator for variation in yields is the standard deviation ( U1) or the annual average variance ( U2) of yields, and the constant relative risk aversion utility function ( U3). We derived two equations to emulate the optimal HCRs with three adjusting parameters corresponding to the management objectives and different magnitudes of estimation errors. These equations will help stakeholders discuss desired management strategies by showing expected catch and risk by adjusting the parameter values.

Robust optimal reinsurance–investment for [formula omitted]-maxmin mean–variance utility under Heston’s SV model

Most literatures about robust optimal reinsurance–investment problem aim to maximum the value function under the worst-case scenario, but some insurers are optimistic, so it is more reasonable to consider a more smooth criterion named α-maxmin criterion which seek a balance between the worst-case scenario and best-case scenario. Furthermore, the past performance of insurance company will heavily impact the reinsurance–investment strategy of insurer, by introducing the capital flow related to the historical performance of the insurer, the wealth process can be described by stochastic delay differential equation. In this paper, we consider the robust optimal reinsurance–investment strategy for an α-maxmin mean–variance insurer with delay under Heston’s stochastic volatility stock model, the verification theorem is given and the closed-form solutions of value function and optimal strategies are obtained, respectively. In the part of numerical analysis, we illustrate the influence of some important parameters on the optimal strategies.

Integrating Risk Preferences into Game Analysis of Price-Making Retailers in Power Market

In the restructured electricity market, retailers are intermediaries between the electricity wholesale market and consumers. Considering the uncertainty of wholesale market price, retailers should consider the risks of their profit caused by the uncertain wholesale price when participating in the retail competition. Indeed, retailers’ risk preferences will impact their price bidding strategies. To examine the effects of retailers’ risk preferences on their strategies and equilibrium outcomes in the retail market, an equilibrium model for price-making retailers is proposed by employing the mean–variance utility theory to model the risk preferences of retailers. The market share function is used to characterize consumers’ price-elasticity and switching behavior in the retail market. Few works in the literature address the issue of bidding strategies of retailers with different risk preferences in the electricity market with switchable consumers. Moreover, the existence and uniqueness of the Nash equilibrium are theoretically proved. A theoretical analysis is presented to investigate the impacts of wholesale price uncertainty and retailer’s risk preference on the bidding strategy. By adopting the nonlinear complementarity approach, the proposed game model is transformed into a set of nonlinear equations, which is further solved by the Levenberg–Marquardt algorithm. Finally, examples are included to verify the effectiveness of the proposed theory, and the results show that the bidding price of a retailer will increase with the increasing uncertainty of the wholesale price and the increasing risk-averse levels of itself and its rivals.

Are banks risk-averse or risk-neutral investors?

In this study, we verify how to construct the utility maximization problem for banks in their asset allocation. We consider two utility maximization problems for the risk-averse and risk-neutral banks to determine the optimal lending ratios to represent banks’ optimal asset allocation. We apply the mean–variance utility for the risk-averse problem and impose the risk constraint for the risk-neutral problem to obtain the optimal solution. In order to validate the model, we investigate how the optimal lending ratios derived from the two models fit the actual bank lending ratio through calibration. Statistical tests for the calibration results do not indicate a significant difference in the model fitting between the risk-averse and risk-neutral models. Hence, this enables us to use both models to describe banks’ asset allocation.

Investor bias, risk and price volatility

PurposeThis study proposes a framework based on salience theory and shows that focusing on one type of risk (idiosyncratic or systemic) can explain overpricing of securities ex ante, and resales at low prices during crisis periods.Design/methodology/approachThe author consider an overlapping generations (OLG) model where each generation lives for two periods and there is no population growth. Agents (investors) start their lives with an endowment W > 0 and have mean-variance utility. They invest their endowment when young and consume when old. Each period, the young investors optimally choose their portfolio from different risky assets acquired from the old generation, all assumed to be in fixed supply.FindingsThe author show that investor salience bias can explain excess volatility of asset prices and the resulting fire-sales in periods of financial turmoil. A change in salience – from one component (idiosyncratic) to the other (systemic) – will generate excess volatility. Interestingly, higher risk aversion generally exacerbates the excess volatility of prices. Moreover, the model predicts that if a big systemic shock hits the financial system, due to salience bias the price of systemic assets falls sharply. This relates to the observed fire-sales of assets during the global financial crisis.Practical implicationsThe proposed model and results suggest that there may be a scope for intervention in financial markets during turbulences. In terms of ex ante policies the study suggests that investors and regulator should use better risk assessment technologies.Originality/valueThis is the first study constructing a tractable model based on the argument that investor salience may exacerbate the excess volatility of prices during financial downturns. The author relate salience to two types of risk; idiosyncratic and systemic and assume that investors' risk perception is biased towards the type of risk that is currently salient based on prior beliefs or past data. The author show that the diversification fallacy of the precrisis period, where seemingly safe assets were overpriced, can be explained by agents overweighing idiosyncratic risk and ignoring systemic risk.

Designing socially optimal rates of tax and rebate structures in directing migration of risk-averse suppliers towards sustainable products

ABSTRACT This study offers design of the ‘socially optimal’ rebate and tax structures, corresponding to the maximum expected gain and minimum risk from migration of prospective risk-averse suppliers towards supplying sustainable products. Risk-averse behaviour is caused by small and medium-sized suppliers who are financially constrained from the perspective of a textile company. This study addresses the unexplored but serious issue of suppliers’ willingness-to-pay for renouncing the option of migrating towards sustainable practices under uncertain market conditions for sustainable products, by using a mean-variance utility framework. The analytical model is validated using case-based real data collected from an Indian retailer who works with two types of suppliers in India: one natural fibre supplier and another chemical-based synthetic fibre supplier. Our model helps explain the effects of loss in expected market share and sudden increase in variability in market share for sustainable products respectively on the ‘socially optimal’ rate of tax and rebate. Also, we establish that with rate of tax increases, the ‘socially optimal’ rate of rebate on sustainable product must increase at an increasing rate to induce potential migration of suppliers towards sustainable practices. The implications of our findings on academics and practice are offered.

Utility basis of consumption and investment decisions in a risk environment.

Using expectations regarding utilities to make decisions in a risk environment hides a paradox, which is called the expected utility enigma. Moreover, the mystery has not been solved yet; an imagined utility function on the risk-return plane has been applied to establish the mean-variance model, but this hypothetical utility function not only lacks foundation, it also holds an internal contradiction. This paper studies these basic problems. Through risk preference VNM condition is proposed to solve the expected utility enigma. How can a utility function satisfy the VNM condition? This is a basic problem that is hard to deal with. Fortunately, it is found in this paper that the VNM utility function can have some concrete forms when individuals have constant relative risk aversion. Furthermore, in order to explore the basis of mean-variance utility, an MV function is founded that is based on the VNM utility function and rooted in underlying investment activities. It is shown that the MV function is just the investor’s utility function on the risk-return plane and that it has normal properties. Finally, the MV function is used to analyze the laws of investment activities in a systematic risk environment. In doing so, a tool, TRR, is used to measure risk aversion tendencies and to weigh risk and return.

Dynamic trading with uncertain exit time and transaction costs in a general Markov market

This paper investigates a dynamic trading problem with transaction cost and uncertain exit time in a general Markov market, where the mean vector and covariance matrix of returns depend on the states of the stochastic market, and the market state is regime switching in a time varying state set. Following the framework proposed by Gârleanu and Pedersen (2013), the investor maximizes his or her multi-period mean–variance utility, net of quadratic transaction costs capturing the linear price impact where trades lead to temporary linear changes in prices. The explicit expression for the optimal strategy is derived by using matrix theory technique and dynamic programming approach. Finally, numerical examples are provided to study the effects of transition cost and exit probability on the wealth process, the trading strategy, turnover rate and the total transaction cost.

평균-분산 효용함수하에서 CAPM의 유도

This article has derived the CAPM under the mean-variance utility function. Thus, it has the following academic significance. Firstly, the article has proposed a new way of deriving the CAPM in addition to the various traditional ones by previous studies of Sharpe(1964), Lintner(1965), Mossin(1966), Huang & Litzenberger(1988), etc. Secondly, by proposing the assumption of mean-variance utility to derive the CAPM, it has contributed to the research on assumptions or conditions for the CAPM such as Markowitz(1959), Tobin(1958, 1969), Borch(1969), Feldstein(1969), Ross(1978), Nielsen(1990), Allingham(1991), Berk(1997), etc. Thirdly, it has proposed an intuitive and simple assumption of mean-variance utility to derive the CAPM unlike the traditional nonintuitive and mathematical assumptions or conditions for the CAPM proposed by preceding researches of Markowitz(1959), Tobin(1958, 1969), Borch(1969), Feldstein(1969), Ross(1978), Nielsen(1990), Allingham(1991), Berk(1997), etc.

Effects of Carbon Policy on Carbon Emission Reduction in Supply Chain under Uncertain Demand

Although there are many articles on carbon emission reduction of sustainable supply chain, most of them study the carbon emission reduction efficiency of supply chain in the case of single carbon policy or demand determination. Based on previous studies, this paper considered a supply chain consisting of a single manufacturer and a single retailer in an uncertain demand market. The effects of demand randomness and different carbon policies on carbon emission reduction level and optimal decision in supply chain were studied by constructing mean-variance utility function and Stackelberg game. Due to the difficulty of data acquisition, this paper verified the equalization results by numerical simulation. The results show that: (1) cap-and-trade policy, government subsidy policy and carbon tax policy can promote the carbon emission reduction investment of supply chain, while carbon tax policy will lead to the decline of the overall profit of supply chain; (2) For the manufacturer and the retailer, adopting a strategy with a low degree of risk avoidance will increase its own profits; (3) For the supply chain as a whole, it is more advantageous for manufacturers to adopt higher risk avoidance strategies, while retailers to adopt lower risk avoidance strategies. In addition, in the conclusion, this paper puts forward management implications related to stakeholders, thus providing help for the development of sustainable supply chain.

Switching Coefficients or Automatic Variable Selection: An Application in Forecasting Commodity Returns

In this paper, we conduct a thorough investigation of the predictive ability of forward and backward stepwise regressions and hidden Markov models for the futures returns of several commodities. The predictive performance relative a standard AR(1) benchmark is assessed under both statistical and economic loss functions. We find that the evidence that either stepwise regressions or hidden Markov models may outperform the benchmark under standard statistical loss functions is rather weak and limited to low-volatility regimes. However, a mean-variance investor that adopts flexible forecasting models (especially stepwise predictive regressions) when building her portfolio, achieves large benefits in terms of realized Sharpe ratios and mean-variance utility compared to an investor employing AR(1) forecasts.