Case Of Risk Aversion Research Articles

Transactive energy framework in fuel cell based multi-carrier energy hubs based on conditional value-at-risk

The prevalence of peer-to-peer operation among industrial energy hubs is considered a promoting method to enhance local energy autonomy, efficiency, and flexibility. By conducting stochastic programming, this paper aims to minimize the operating cost of multiple industrial energy hubs that trade power and heat energies with each other and utility. Concerning the important role of hydrogen systems, fuel cell-based combined heat and power (CHP) generators are employed within the hubs to increase sustainability. The presence of electric vehicles (EVs) and shiftable loads enhances the flexibility during peer-to-peer operating mode. The trading price for power and heat energies are derived at first by solving a deterministic problem and considering average values for demands and generation. However, to address the uncertainties in renewable generation, electric and heat demands, and electricity prices under operation, scenario-based stochastic programming tries to optimize the expected objective function. Furthermore, the Conditional Value-at-Risk (CVaR) approach is proposed to provide various risk-averse scheduling tactics and measure the risk of each scenario. The results show that the proposed risk-constrained approach reduces the risk and makes cautious decisions about energy resources and trades. In this regard, the expected profit has been reduced by 75%, i.e., from 1636.78 NOK under a risk-neutral case to 414.97 NOK under a risk-averse case to reduce the expected risk in operating cost.

OPTIMAL INVESTMENT POLICY AND CAPITAL MANAGEMENT IN A FINANCIAL INSTITUTION

This research work considered an asset optimization problem where we examine how a financial institution can optimally allocate its total wealth among three assets namely; treasury, security and loan in stochastic interest rate setting and also determined how a financial institution can manage its capital. The optimal investment policy was derived through the application of stochastic optimization theory for the case of constant relative risk aversion (CRRA) utility function. Also, the Stochastic Differential Equation (SDE) for the capital adequacy ratio under Basel Accord, the SDE for the Total Risk – Weighted Assets (TRWA), the SDEs for the capital required to maintain the capital adequacy ratio under Basel II and Central Bank of Nigeria (CBN) standards were derived and solved numerically to study the capital management problem of the financial institution. Numerical examples using published data obtained from Central Bank of Nigeria (CBN) statistical bulletin and Nigeria Stock Exchange were presented to illustrate the dynamics of the optimal investment policy and how a financial institution can manage its capital. From the results, the optimal investment strategy can be achieved by shifting the financial institution investment away from the risky assets (security and loan) towards the riskless asset (treasury). It was also observed that if a financial institution observes the Basel II standard or Nigeria CBN standard of capital requirement, the financial institution would be considered to be strongly capitalized and guarantees the ability to absorb unexpected losses.

Portfolios of value and momentum: disappointment aversion and non-normalities

Professional money managers often combine value and momentum to benefit from diversification gains resulting from their negative return correlation. We go beyond the mean-variance and constant relative risk aversion environments to investigate this fundamental issue by assuming that investors exhibit disappointment aversion, and empirically account for the non-normalities and non-linear dependencies of the returns associated with these strategies. We perform an exploration exercise on the interplay of these two general sets of assumptions. In accordance with the literature, we find that disappointment preferences lead to optimal portfolio choices that are not attainable under the traditional constant relative risk aversion case. The findings reveal that higher disappointment aversion utility levels can be reached when non-normalities are introduced in the optimization process. The intensity of this phenomenon rises as disappointment aversion increases. However, taking advantage of these non-linearities and non-normalities requires higher portfolio turnovers. Therefore, when introducing transaction costs in the analysis, we find significant improvement in certainty equivalent returns only for investors having high disappointment aversion levels and facing low transaction costs.

A combined forecasting and packing model for air cargo loading: A risk-averse framework

In this paper, we present a combined forecasting and optimization decision-support tool to assist air cargo revenue management departments in the acceptance/rejection process of incoming cargo bookings. We consider the case of a combination airline and focus on the passenger aircraft belly capacity. The process is dynamic (bookings are received in a discrete fashion during the booking horizon) and uncertain (for some bookings the three dimensions are not provided, while the actual belly space available for cargo is only revealed a few hours before departure). Hence, analysts base decisions on historical data or human experience, which might yield sub-optimal or infeasible solutions due to the aforementioned uncertainties. We tackle them by proposing data-driven algorithms to predict available cargo space and shipment dimensions. A packing problem is solved sequentially once a new booking request is received, predicting shipment dimensions, if necessary, and considering the uncertainty of such prediction. The booking is accepted if it results in a feasible loading configuration where no previously accepted booking is offloaded. When applied in a deterministic context, our packing method outperformed the one used by the partner airline, increasing the loaded volume up to 20%. The framework was also tested assuming unknown shipment dimensions, comparing a risk-prone and a risk-averse strategy, with the latter accounting for uncertainty in dimension predictions and the former using mean values. While the average loaded volume decreases in the risk-averse case, the number of unplanned offloadings due to under-predicted dimensions decreases from 54% to 12% of the simulated cases, hence yielding a more robust acceptance strategy.

Mean-variance versus utility maximization revisited: The case of constant relative risk aversion

We examine if mean-variance (M-V) is a good proxy for portfolios based on the Constant Relative Risk Aversion (CRRA) utility function. M-V portfolios are considered good proxies for portfolios from several utility functions which is why they are routinely used in the portfolio theory literature as the benchmark. Our results clearly show this is not the case. Low risk CRRA portfolios are in many cases very different to M-V portfolios, especially with respect to downside risk. If a risk-free asset is available, in many cases, no M-V portfolio is an adequate proxy for CRRA portfolios. The implications of our findings are that: i) M-V portfolios are a poor proxy for investors with CRRA preferences, ii) CRRA portfolios are more suited to investors who care about downside risk than M-V portfolios, and iii) the efficacy of M-V to proxy for utility maximization should be examined more thoroughly.

Information gap decision theory for operation of combined cooling, heat and power microgrids with battery charging stations

The role of combined cooling heat and power (CCHP) microgrids (MGs) in sustainable cities, due to high penetration of renewables and coordinated supply of different energy demands, is significant. CCHP MGs have energy management systems that conduct unit commitment (UC). In this research, a risk-aware information gap decision theory (IGDT)-based energy management system is developed for CCHP MGs with battery charging stations, considering ON/OFF history of power/heat/cooling units, minimum up-time and minimum down-time constraints, start-up and shut-down ramp rate limits. The schedule of components in CCHP MG is determined from the view of risk-seeker and risk-averse decision maker and is compared with the case in which the uncertainties are ignored. In this research, the uncertainties of demands and wind power are taken into account. The operation of CCHP MG is modeled as a mixed-integer linear problem (MILP) and is solved with CPLEX solver. The case study is an isolated wind-integrated CCHP MG with power generation units, combined heat and power (CHP) units, boiler, heat recovery unit, absorption chiller, electric chiller, battery charging station, storage systems and adjustable electric, thermal and cooling loads. In risk-averse IGDT-based UC, a robust scheduling with respect to uncertainties of electric, thermal and cooling demand and wind power is achieved; in this way, the decision maker is sure that no realization of uncertain parameters in real-time may result in an operation cost above critical operation cost. For instance, in the case considering the uncertainty of electric demand, MG operation cost will not exceed $1568.8586 if real-time realization of electric demands fall within the 6.7% band around nominal electric demands. On the other hand, risk-seeking IGDT determines the least needed deviation of different uncertain parameters which make a target operation cost accessible; in this way, the best realization of uncertain parameters in real-time results in an operation cost equal to the target operation cost. The results for risk-seeking and risk-averse cases are compared and the impact of risk on the schedule of MG components is meticulously investigated.

Disappointment aversion in tournaments

AbstractMany experiments and field studies indicate that individuals have an asymmetric attitude towards gains versus losses. In this paper, we extend the canonic tournament model by assuming the workers' preferences exhibit disappointment aversion. First, we find the winning prize is first increasing and then decreasing in volatility and the losing prize shows the opposite. Furthermore, when the volatility exceeds a threshold, both the winning and losing prizes are reduced to zero. By contrast, there is no such kink for the risk aversion case. Finally, we find the piece rates always dominate rank‐order tournaments when the workers are disappointment averse.

Risk‐averse integrated demand response and dynamic G2V charge scheduling of an electric vehicle aggregator to support grid stability

Electric vehicle aggregator (EVA) trades in energy and ancillary service markets for profit maximisation through grid-to-vehicle (G2V) charge scheduling of EVs. It can provide regulation services to system operator (SO) through coordinated and distributed charging of EVs. However, EV owner aim at minimum charging cost. Price-based demand response (PBDR) integrated charge scheduling can motivate EVs by off peak charging for reduced cost along with system load levelling. Real-time (RT) PBDR, adopted in literature, has low acceptance rate by EVs for being too dynamic to respond and being infeasible for few charge cycles in a day. Time of use (TOU) PBDR, being less dynamic, is a natural price signal for EVs and shields them from RTP volatility as well. Additionally, EV charging cost constrained EVA's charge scheduling is a realistic formulation and is subjected to multiple uncertainties like EVs' mobility behaviour and market prices. Considering this, risk-averse charge scheduling of EVA with TOU PBDR and EV charging cost constraint is proposed. EVs' mobility behaviour and market prices' uncertainties are modeled through stochastic programming. Agglomerative hierarchical clustering is proposed to develop TOU price for EVA from RTP. Conditional value at risk (CVaR) is used as risk measure. Results of a case study of EVA with 1000 EVs illustrate a trade-off among EVA profit and risk with optimal values of EV charging cost and regulation provision to SO for risk-neutral and risk-averse cases.

Welfare with Imperfect Foreknowledge: The Case of Risk Aversion

We study the use of discrete choice models in the context of recreation when there may be discrepancy between the anticipated (ex ante) and the experienced quality of site attributes due to imperfect information. Unlike previous literature on the topic, we relax the assumption of risk neutrality. Adopting a model with quasi-linear preferences, we characterize the disparity between ex ante and ex post utility by decomposing expected utility into a term stemming from bias in beliefs and a component representing willingness to pay for reducing uncertainty in site attributes. Our results show that ex post corrections of welfare losses are attenuated by greater dispersion in beliefs about amenities.

On the dynamics of stock price bubbles: comments on a model by Miao and Wang

We consider the model by Miao and Wang (Am Econ Rev 108:2590–2628, 2018), in which endogenous collateral constraints may generate stock price bubbles. Whereas Miao and Wang (2018) characterize the local dynamics around stationary equilibria only under the assumption of risk neutral households, we extend this characterization to the case of risk aversion.

User cost of credit card services under risk with intertemporal nonseparability

This paper derives the user cost of monetary assets and credit card services with interest rate risk under the assumption of intertemporal non-separability. Barnett and Su (2016) derived theory permitting inclusion of credit card transaction services into Divisia monetary aggregates. The risk adjustment in their theory is based on consumption capital asset pricing model (CCAPM) under intertemporal separability. The equity premium puzzle focusses on downward bias in the CCAPM risk adjustment to common stock returns. Despite the high risk of credit card interest rates, the risk adjustment under the CCAPM assumption of intertemporal separability might nevertheless be similarly small. While the known downward bias of CCAPM risk adjustments are of little concern with Divisia monetary aggregates containing only low risk monetary assets, that downward bias cannot be ignored, once high risk credit card services are included. We believe that extending to intertemporal non-separability could provide a non-negligible risk adjustment, as has been emphasized by Barnett and Wu (2015).In this paper, we extend the credit-card-augmented Divisia monetary quantity aggregates to the case of risk aversion and intertemporal non-separability in consumption. Our results are for the “representative consumer” aggregated over all consumers. While credit-card interest-rate risk may be low for some consumers, the volatility of credit card interest rates for the representative consumer is high, as reflected by the high volatility of the Federal Reserve’s data on credit card interest rates aggregated over consumers. One method of introducing intertemporal non-separability is to assume habit formation. We explore that possibility.

Geometric Dispersion Theory for Portfolio Accurate Out-of-Sample Predictions of Stock Market

This paper addresses portfolio selection under Geometric Dispersion Theory (GDT). GDT is a recently developed model for analyzing risk. GDT evaluates the risk of each alternative based on two new geometric dispersion measures; one for the risk-prone case and one for the risk-averse case. GDT risk measures satisfy convexity, non-negativity, and asymmetry where other models ignore the last property. Also, GDT model satisfies first-order stochastic dominance and resolves drawbacks of other decision-making models. GDT outperforms Mean-Variance, Expected utility theory, and Cumulative Prospect theory. In this study, we apply GDT for portfolio selection problem and compare it to Mean-Variance, Mean-absolute Deviation, Two-Sided Coherent Risk Measure. We show that GDT risk measures satisfy all of the desirable properties of risk measure including diversification, monotonicity, insensitivity to mean preserving spread, and asymmetry while other risk measures do not satisfy all of these properties. Also, we compare performances of the models based on real-world data and show that GDT models outperform the models in term of the diversification ratio and in out-of-sample data, GDT models outperform the models in term of tracking error, information ratio, Sharpe Ratio and expected returns rate of portfolios.

Design under uncertainty of carbon capture, utilization and storage infrastructure considering profit, environmental impact, and risk preference

This study presents a decision making tool for risk management of a carbon capture utilization and storage (CCUS) network under uncertainty among conflicting objectives. A two-phase-two-stage stochastic multi-objective optimization problem solving algorithm is formulated to balance environmental impact and various sources of uncertainty and corresponding risk by installing and operating a CCUS network. The algorithm allows decision makers to choose their own tolerance on risk. By conducting case studies that have different target profits for CCUS networks, the algorithm provides optimal results based on the decision maker’s attitude to risk. To evaluate risks imposed by uncertain parameters, a concept of downside risk is introduced. By setting different target profit levels, the suggested tool enables decision makers to choose their own tolerance and preference for risk. In the model, the life cycle assessment is applied to evaluate all environmental contributions caused by installation and operations of the CCUS network. The model provides the trade-off relationship between total annual benefit with financial risk as well as corresponding environmental impact. The aim of this model to optimize CCUS supply chain networks is to provide an intuitive decision making algorithm to balance conflicting objectives within a single framework. This problem is formulated as a mixed integer linear program model. To illustrate the applicability of the model, four optimal CCUS network models for the various types of industrial complex of Korea in 2030 are presented. Results indicate that risk-averse cases with a low profit target are more reliable in stochastic uncertainty, and that risk-taking decision makers tend to invest more on capture facility and produce more product than do, risk-averse decision makers.

Optimal Price-Energy Demand Bids for Aggregate Price-Responsive Loads

In this paper, we seek to optimally operate a retailer that, on one side, aggregates a group of price-responsive loads and on the other, submits block-wise demand bids to the day-ahead and real-time markets. Such a retailer/aggregator needs to tackle uncertainty both in customer behavior and wholesale electricity markets. The goal in our design is to maximize the profit for the retailer/aggregator. We derive closed-form solutions for the risk-neutral case and also provide a stochastic optimization framework to efficiently analyze the risk-averse case. In the latter, the price-responsiveness of the load is modeled by means of a non-parametric analysis of experimental random scenarios, allowing for the response model to be non-linear. The price-responsive load models are derived based on the Olympic Peninsula experiment load elasticity data. We benchmark the proposed method using data from the California ISO wholesale electricity market.

Scenario reduction for stochastic programs with Conditional Value-at-Risk

In this paper we discuss scenario reduction methods for risk-averse stochastic optimization problems. Scenario reduction techniques have received some attention in the literature and are used by practitioners, as such methods allow for an approximation of the random variables in the problem with a moderate number of scenarios, which in turn make the optimization problem easier to solve. The majority of works for scenario reduction are designed for classical risk-neutral stochastic optimization problems; however, it is intuitive that in the risk-averse case one is more concerned with scenarios that correspond to high cost. By building upon the notion of effective scenarios recently introduced in the literature, we formalize that intuitive idea and propose a scenario reduction technique for stochastic optimization problems where the objective function is a Conditional Value-at-Risk. Numerical results presented with problems from the literature illustrate the performance of the method and indicate the cases where we expect it to perform well.

Online-Appendix to: Making Parametric Portfolio Policies Work: Comments on Brandt, Santa-Clara and Valkanov (2009)

We provide examples of pitfalls for parametric portfolio policies as introduced by Brandt, Santa Clara and Valkanov. For the leading case of constant relative risk aversion (CRRA) strong assumptions on the properties of the returns, the variables used to implement the parametric portfolio policy and the parameter space are necessary to obtain a well defined optimization problem. As possible remedies for practical work various extensions of CRRA Bernoulli utility to the real line are discussed. Also prospect theory is suggested as an alternative approach. We observe that for low levels of relative risk aversion expected utility turns non-monotonic and an interior maximum need not exist. We provide economic conditions that overcome such empirical problems and that guarantee the effectiveness of the approach more broadly. We illustrate our concerns by applying parametric portfolio policies to a large universe of stocks. Full paper is available at: https://ssrn.com/abstract=3081100

Dynamic relational contracts under complete information

This paper considers a long-term relationship between two agents who both undertake an action or investment that produces a joint benefit. Agents have an opportunity to expropriate some of the joint benefit for their own use. Agents have quasi-linear preferences. Two cases are considered: where agents are risk averse but where limited liability constraints do not bind, and where agents are risk neutral and subject to limited liability constraints. We ask how to structure the investments and division of the surplus over time to avoid expropriation. In the risk-averse case, the dynamics of actions and surplus may or may not be monotonic depending on whether or not a first-best allocation can be sustained. Agents may underinvest but never overinvest. If the first-best allocation is not sustainable, there is a trade-off between risk sharing and surplus maximization; surplus may not be at its constrained maximum even in the long run and the “amnesia” property of pure risk-sharing models fails to hold. In contrast, in the risk-neutral case there may be an initial phase in which one agent overinvests and the other underinvests. Both actions and surplus converge monotonically to a stationary state, where surplus is maximized subject to the self-enforcing constraints.

An Optimal Consumption Problem for General Factor Models

We consider the Merton consumption problem on a finite time horizon to optimize the discounted expected power utility of consumption and terminal wealth in risk-averse cases. The returns and volatilities of the assets are random and affected by some economic factors, modeled as a diffusion process. The problem becomes a standard stochastic control problem. We derive the Hamilton--Jacobi--Bellman (HJB) equation and study its solutions. Under general conditions we construct a suitable subsolution--supersolution pair. We prove the existence and uniqueness of solution for this HJB equation. Finally, we show the verification theorem.

Time-Consistent Mean-Variance Reinsurance-Investment Problems Under Unbounded Random Parameters: BSDE and Uniqueness

To strike the best balance between insurance risk and profit, insurers transfer insurable risk through reinsurance and enhance yield by participating into the financial market. The long-term commitment of insurance contracts makes insurers necessary to consider time-consistent (TC) reinsurance-investment policies. Using the open-loop TC mean-variance (MV) reinsurance-investment framework, we investigate the equilibrium reinsurance-investment problems for the financial market with unbounded random coefficients or, specifically, an unbounded risk premium. We characterize the problem via a backward stochastic differential equation (BSDE) framework. An explicit solution to the equilibrium strategies is derived for a constant risk aversion under a general class of stochastic models, embracing the constant elasticity of variance (CEV) and Ornstein-Uhlenbeck (OU) processes as special cases. For state-dependent risk aversions, the problem is related to the existence of a solution to a quadratic BSDE with unbounded parameters. A semi-closed form solution is derived, up to the solution to a nonlinear partial differential equation. By examining properties of the equilibrium strategies numerically, we find that the reinsurance decision is greatly affected by the market situation under the state-dependent risk aversion case. We prove the uniqueness of equilibrium strategies for both cases.

Making Parametric Portfolio Policies Work: Comments on Brandt, Santa-Clara and Valkanov (2009)

We provide examples of pitfalls for parametric portfolio policies as introduced by Brandt, Santa Clara and Valkanov (RFS 2009). For the leading case of constant relative risk aversion (CRRA) strong assumptions on the properties of the returns, the variables used to implement the parametric portfolio policy and the parameter space are necessary to obtain a well defined optimization problem. As possible remedies for practical work various extensions of CRRA Bernoulli utility to the real line are discussed. Also prospect theory is suggested as an alternative approach. We observe that for low levels of relative risk aversion expected utility turns non-monotonic and an interior maximum need not exist. We provide economic conditions that overcome such empirical problems and that guarantee the effectiveness of the approach more broadly. We illustrate our concerns by applying parametric portfolio policies to a large universe of stocks. Appendix is available at: https://ssrn.com/abstract=3131081