Risk-neutral Model Research Articles

Application of robust information game decision theory for risk-assessment problem in large scale users

This work suggested a novel method in order to solve uncertain problem with uncertainty on pool market tariff with respect to wind and photovoltaic generations as well as storage units. Aiming this regard, information gap decision theory method is applied for solving the considered problem. This way, 3 major models are considered into account for big industrial consumers including: risk-taker, risk-averse, and risk-neutral models. Efficiency of suggested methods are studied by exertion of proposed method on big consumer risk via various pool yield tariffs. In addition, appraised obtained results prove the efficiency of demand response program for decreasing the over expenditure of big consumer. Therefore, good impacts of demand response program caused decrease in big user expenditure.

Designing a resilient and reliable biomass-to-biofuel supply chain under risk pooling and congestion effects and fleet management

The utilization of renewable biomass as feedstock for biofuel production has been gaining prestige to mitigate carbon emissions. This paper aims to render an optimization model for designing a resilient and reliable biomass-to-biofuel supply chain network in which multi-modal terminals, biorefineries, and their connection link could be faced with disruption. For this purpose, risk-averse optimization, transitional probabilities, and spatial statistics models are employed. What is more, to overcome the repercussions of uncertain demand and the availability of raw materials, risk pooling and M/M/1 queuing system are considered. Finally, since the proposed model is an NP-hard problem, two meta-heuristic algorithms called improved ray optimization and colliding bodies optimization are employed to solve the proposed model. Computational results reveal that by increasing 20% of the conversion rate of biomass to biofuel, which leads to increase biomass supply, biofuel production increases by 20.88%, and the SC cost declines by 9.32% due to the better capacity distribution of bio-refineries. Also, the proposed model increases by 20.87% in the total SC costs under random disruptions than the risk-neutral model, although the failure costs of SC decline by 80.45%.

Risk-averse outsourcing strategy in the presence of demand and supply uncertainties

This study investigates an outsourcing strategy for a risk-averse decision-maker facing two types of demand and supply uncertainties. The supply uncertainty includes both uncertainty in the rate of capacity allocation in the manufacturer and the uncertainty resulting from disruption risks. In order to capture the geographical characteristics of the suppliers, we assume that the suppliers belong to two different geographical regions: the manufacturer’s region (domestic supplier) and outside of the manufacturer’s region (foreign supplier). We also consider a realistic scenario in which the manufacturer and domestic suppliers might face two types of disruption:(i) local disruption which might occur inside the suppliers or manufacturer’s facility such as disruption in the production line, and (ii) regional disruption which might occur in the region of the domestic supplier and manufacture simultaneously, such as natural hazards. To provide a benchmark, at first, the risk-neutral model is analyzed and then the risk-averse model is developed to consider the risk attitude of the decision-maker. In the latter case, we apply two types of risk evaluation model to analyze the decision maker’s behavior: value-at-risk (VaR) and conditional value-at-risk (CVaR). In addition, we solve optimally both risk-neutral and risk-averse models by deriving Karuch–Kuhn–Tucker (K.K.T) optimality condition. Computational examples illustrate the impact of decision-maker attitude on the manufacture’s outsourcing strategy. In addition, the sensitivity of the optimal outsourcing decisions with regards to the important parameters of the model is analyzed.

Eco-friendly container transshipment route scheduling problem with repacking operations

Currently, a huge amount of cargo is transported via containers by liner shipping companies. Under stochastic demand, repacking operations and carbon reduction, which may lead to an increase in effectiveness and environmental improvement, have been rarely considered in previous literature. In this paper, we investigate a container transshipment route scheduling problem with repacking operations under stochastic demand and environmental protection. The problem is a combinatorial optimization problem. Lacking historical data, a chance-constrained programming model is proposed to minimize the total operating and environment-related costs. We choose two distribution-free approaches, i.e., approximation based in Markov’s Inequality and Mixed Integer Second-Order Conic Program to approximate the chance constraints. As the loses induced by unfulfilled demand are not taken into account in the above model, a scenario-based model is developed considering the loses. Risk-neutral model may provide solutions that perform poorly while considering uncertainty. To incorporate decision makers’ perspectives, therefore, we also propose a risk-averse model adopting a risk aversion measure called Conditional Value-at-Risk to meet different preferences. Finally, we conduct computational experiments based on real data to compare the performances of the modeling methods and illustrate the impacts by testing different risk levels and confidence levels.

Reference-Dependent Preferences and Overbidding in Private and Common Value Auctions

This paper proposes a model of reference dependent preferences to explain overbidding in private and common value auctions. It is assumed that the reference point is proportional to the value of the object and that losses are weighed more heavily than gains in the utility function. Equilibrium bidding strategies are derived for first- and second-price private and common value auctions. I find that this model fits the data of all experiments analyzed, both private and common value, better in terms of the Bayesian Information Criterion than a standard risk neutral model; moreover, it explains overbidding in all private value and some common value auctions better than other alternative models. These results suggest that reference dependence, among other factors, might play a role in the widespread tendency of subjects to overbid in most experimental auctions.

The leverage effect puzzle revisited: Identification in discrete time

The term “leverage effect,” as coined by Black (1976), refers to the tendency of an asset’s volatility to be negatively correlated with the asset’s return. Aït-Sahalia et al. (2013) refer to the “leverage effect puzzle” as the fact that, in spite of a broad agreement that the effect should be present, it is hard to identify empirically. For this purpose, we propose an extension with leverage effect of the discrete time stochastic volatility model of Darolles et al. (2006). This extension is shown to be the natural discrete time analog of the Heston (1993) option pricing model. It shares with Heston (1993) the advantage of structure preserving change of measure: with an exponentially affine stochastic discount factor, the historical and the risk neutral models belong to the same family of joint probability distributions for return and volatility processes. The discrete time approach allows us to make the role of various parameters more transparent: leverage versus volatility feedback effect, connection with daily realized volatility, impact of leverage on the volatility smile, etc. Even more importantly it sheds some new light on the identification of leverage effect and of the various risk premium parameters through link functions in closed form. The price of volatility risk is identified from underlying asset return data, even without option price data, if and only if leverage effect is present. However, the link functions are almost flat if the leverage effect is close to zero, making estimation of the volatility risk price difficult and paving the way for identification robust inference.

An optimal control of a risk-sensitive problem for backward doubly stochastic differential equations with applications

Abstract In this paper, we are concerned with an optimal control problem where the system is driven by a backward doubly stochastic differential equation with risk-sensitive performance functional. We generalized the result of Chala [A. Chala, Pontryagin’s risk-sensitive stochastic maximum principle for backward stochastic differential equations with application, Bull. Braz. Math. Soc. (N. S.) 48 2017, 3, 399–411] to a backward doubly stochastic differential equation by using the same contribution of Djehiche, Tembine and Tempone in [B. Djehiche, H. Tembine and R. Tempone, A stochastic maximum principle for risk-sensitive mean-field type control, IEEE Trans. Automat. Control 60 2015, 10, 2640–2649]. We use the risk-neutral model for which an optimal solution exists as a preliminary step. This is an extension of an initial control system in this type of problem, where an admissible controls set is convex. We establish necessary as well as sufficient optimality conditions for the risk-sensitive performance functional control problem. We illustrate the paper by giving two different examples for a linear quadratic system, and a numerical application as second example.

Identification and Inference in First-Price Auctions with Risk Averse Bidders and Selective Entry

We study identification and inference in first-price auctions with risk averse bidders and selective entry, building on a flexible entry and bidding framework we call the Affiliated Signal with Risk Aversion (AS-RA) model. Assuming that the econometrician observes either exogenous variation in the number of potential bidders (N) or a continuous instrument (z) shifting opportunity costs of entry, we provide a sharp characterization of the nonparametric restrictions implied by equilibrium bidding. Given variation in either competition or costs, this characterization implies that risk neutrality is nonparametrically testable in the sense that if bidders are strictly risk averse, then no risk neutral model can rationalize the data. In addition, if both instruments (discrete N and continuous z) are available, then the model primitives are nonparametrically point identified. We then explore inference based on these identification results, focusing on set inference and testing when primitives are set identified. Keywords: Auctions, entry, risk aversion, identification, set inference.

On stochastic maximum principle for risk-sensitive of fully coupled forward-backward stochastic control of mean-field type with application

In this paper, we are concerned with an optimal control problem where the system is driven by fully coupled forward-backward stochastic differential equation of mean-field type with risk-sensitive performance functional. We study the risk-neutral model for which an optimal solution exists as a preliminary step. This is an extension of the initial stochastic control problem in this type of risk-sensitive performance problem, where an admissible set of controls are convex. We establish necessary as well as sufficient optimality conditions for the risk-sensitive performance functional control problem. Finally, we illustrate our main result of this paper by giving two examples of risk-sensitive control problem under linear stochastic dynamics with exponential quadratic cost function, the second example will be a mean-variance portfolio with a recursive utility functional optimization problem involving optimal control. The explicit expression of the optimal portfolio selection strategy is obtained in the state feedback.

A Risk-Averse Shelter Location and Evacuation Routing Assignment Problem in an Uncertain Environment.

Disasters such as hurricanes, earthquakes and floods continue to have devastating socioeconomic impacts and endanger millions of lives. Shelters are safe zones that protect victims from possible damage, and evacuation routes are the paths from disaster zones toward shelter areas. To enable the timely evacuation of disaster zones, decisions regarding shelter location and routing assignment (i.e., traffic assignment) should be considered simultaneously. In this work, we propose a risk-averse stochastic programming model with a chance constraint that takes into account the uncertainty in the demand of disaster sites while minimizing the total evacuation time. The total evacuation time reflects the efficacy of emergency management from a system optimal (SO) perspective. A conditional value-at-risk (CVaR) is incorporated into the objective function to account for risk measures in the presence of uncertain post-disaster demand. We resolve the non-linear travel time function of traffic flow by employing a second-order cone programming (SOCP) approach and linearizing the non-linear chance constraints into a new mixed-integer linear programming (MILP) reformulation so that the problem can be directly solved by state-of-the-art optimization solvers. We illustrate the application of our model using two case studies. The first case study is used to demonstrate the difference between a risk-neutral model and our proposed model. An extensive computational study provides practical insight into the proposed modeling approach using another case study concerning the Black Saturday bushfire in Australia.

On Risk-Averse Stochastic Semidefinite Programs with Continuous Recourse

The vast majority of the literature on stochastic semidefinite programs (stochastic SDPs) with recourse is concerned with risk-neutral models. In this paper, we introduce mean-risk models for stochastic SDPs and study structural properties as convexity and (Lipschitz) continuity. Special emphasis is placed on stability with respect to changes of the underlying probability distribution. Perturbations of the true distribution may arise from incomplete information or working with (finite discrete) approximations for the sake of computational efficiency. We discuss extended formulations for stochastic SDPs under finite discrete distributions, which turn out to be deterministic (mixed-integer) SDPs that are (almost) block-structured for many popular risk measures.

Call Option Pricing Model and Recovery Theorem: A Specific Case of Pricing Warrants

Warrant is normally priced on the basis of Black and Scholes' model, which refers to calculations in a risk neutral world. Hence, it neither captures the market expectation nor being a good reference for the risk management process. This study examines a new way of pricing warrants under the real world probability by utilizing the recovered Vacisek short rate model. Applying Carr and Yu's recovery model, an extended version of Ross Recovery Theorem, we managed to recover the Vasisek process. Then, suppose that the economy is driven by this recovered Vacisek process, we point out a valuation model for the warrant of an underlying stock. We deduce that by applying the recovered Vacisek model we can derive the warrant price under the real world probability without the assumption of the market price of risk as in the risk neutral model.

Data-Driven Stochastic Scheduling for Energy Integrated Systems

As the penetration of intermittent renewable energy increases and unexpected market behaviors continue to occur, new challenges arise for system operators to ensure cost effectiveness while maintaining system reliability under uncertainties. To systematically address these uncertainties and challenges, innovative advanced methods and approaches are needed. Motivated by these, in this paper, we consider an energy integrated system with renewable energy and pumped-storage units involved. In addition, we propose a data-driven risk-averse two-stage stochastic model that considers the features of forbidden zones and dynamic ramping rate limits. This model minimizes the total cost against the worst-case distribution in the confidence set built for an unknown distribution and constructed based on data. Our numerical experiments show how pumped-storage units contribute to the system, how inclusions of the aforementioned two features improve the reliability of the system, and how our proposed data-driven model converges to a risk-neutral model with historical data.

Primal-Dual Learning Based Risk-Averse Optimal Integrated Allocation of Hybrid Energy Generation Plants under Uncertainty

A groundswell of opinion in utilizing environmentally friendly energy technologies has been put forth worldwide. In this paper, we consider an energy generation plant distribution and allocation problem under uncertainty to get the utmost out of available developments, as well as to control costs and greenhouse emissions. Different clean and traditional energy technologies are considered in this paper. In particular, we present a risk-averse stochastic mixed-integer linear programming (MILP) model to minimize the total expected costs and control the risk of CO2 emissions exceeding a certain budget. We employ the conditional value-at-risk (CVaR) model to represent risk preference and risk constraint of emissions. We prove that our risk-averse model can be equivalent to the traditional risk-neutral model under certain conditions. Moreover, we suggest that the risk-averse model can provide solutions generating less CO2 than traditional models. To handle the computational difficulty in uncertain scenarios, we propose a Lagrange primal-dual learning algorithm to solve the model. We show that the algorithm allows the probability distribution of uncertainty to be unknown, and that desirable approximation can be achieved by utilizing historical data. Finally, an experiment is presented to demonstrate the performance of our method. The risk-averse model encourages the expansion of clean energy plants over traditional models for the reduction CO2 emissions.

Pricing temperature derivatives with a filtered historical simulation approach

ABSTRACTIn this paper, we propose pricing temperature derivatives using a filtered historical simulation (FHS) approach that amalgamates model-based treatment of volatility and empirical innovation density. The FHS approach implicitly captures the risk premium with the entire risk-neutral model (except the innovation distribution), thereby providing significantly more flexibility than existing methods that use only one designated parameter to capture the risk premium. Additionally, instead of relying on the fitted innovation distribution, the FHS approach uses empirical innovations to capture excess skewness, excess kurtosis, and other non-standard features in the temperature data, all of which are important for the correct pricing of temperature derivatives. We apply the FHS approach to pricing derivatives written on the temperature of Chicago, and demonstrate that this approach yields better in-sample and out-of-sample pricing performance than the constant market price of risk method and the consumption-based method.

Advanced model calibration on bitcoin options

In this paper, we investigate the dynamics of the bitcoin (BTC) price through the vanilla options available on the market. We calibrate a series of Markov models on the option surface. In particular, we consider the Black–Scholes model, Laplace model, five variance gamma-related models and the Heston model. We examine their pricing performance and the optimal risk-neutral model parameters over a period of 2 months. We conclude with a study of the implied liquidity of BTC call options, based on conic finance theory.

Robust design of a strategic network planning for photovoltaic module recycling considering reclaimed resource price uncertainty

PhotoVoltaic (PV) power is one of the rapidly growing solar energy technologies worldwide. The installed PV power capacity has considerably increased over the past decades. Consequently, the End-of-Life management of used PV modules is becoming very urgent. This article investigates strategic recycling network planning for recycling PV module considering reclaimed resource price uncertainty. Based on a real case setting, the problem is first formulated as a risk-neutral model and then extended to a risk-averse model that considers the risk preferences of investors. Moreover, robust reformulations of the risk-neutral/risk-averse models are proposed to hedge against ambiguity in the probability distribution of the uncertain resource price. An outer approximation based solution approach is proposed to solve the robust reformulations. Numerical experiments with test data generated from the real case are carried out to demonstrate the benefits of the resulting robust model and managerial insights are explored. Lastly, conclusions are drawn and future research directions are outlined.

Resilient Configuration Approach of Integrated Community Energy System Considering Integrated Demand Response Under Uncertainty

Integrated community energy system (ICES) enables multi-energy synergy and impulses interaction of integrated demand response (IDR) from the demand side. Nevertheless, the randomness lies in IDR resources and renewable generation in the ICES configuration issue still lacks thorough analysis. Furthermore, the widely focused concern of resiliency urges more proactive consideration of potential emergencies at the planning stage of ICES. To this end, this paper proposed a resilience-oriented stochastic ICES configuration framework considering IDR influence. First, generalized IDR models are set up in detail with elaborate fuzzy feature analysis of price-responsive multi-energy loads. Then, the vulnerability indicators of tie lines and converting devices of the ICES are first introduced to demonstrate the occasional outage in the normal operation and blackout in the emergent case. In addition, the worst-case conditional value-at-risk (WCVaR) theory is innovatively integrated to the traditional risk-neutral model, which is formulated as a two-stage stochastic chance-constrained programming problem, aiming to combine portfolio with minimizing the worst-case cost caused by a disaster. The models are then transformed into mixed-integer linear programming problems via several linearization techniques. Finally, the results of the case studies showed the established model’s superiority in improving the overall economy (reduce 6.94% of the worst-case cost) and system resiliency (decrease the value-at-risk by 3.20%) against an unforeseen hurricane. Meanwhile, the ICES reliability was also improved by declining 25.65% of unintended load curtailment faced with an emergency. The proposed approach provided an efficient preventive portfolio scheme of the IDR-integrated ICES for decision-makers’ different risk preferences of natural hazards.

Risk-sensitive average optimality in Markov decision processes

In this note attention is focused on finding policies optimizing risk-sensitive optimality criteria in Markov decision chains. To this end we assume that the total reward generated by the Markov process is evaluated by an exponential utility function with a given risk-sensitive coefficient. The ratio of the first two moments depends on the value of the risk-sensitive coefficient; if the risk-sensitive coefficient is equal to zero we speak on risk-neutral models. Observe that the first moment of the generated reward corresponds to the expectation of the total reward and the second central moment of the reward variance. For communicating Markov processes and for some specific classes of unichain processes long run risk-sensitive average reward is independent of the starting state. In this note we present necessary and sufficient condition for existence of optimal policies independent of the starting state in unichain models and characterize the class of average risk-sensitive optimal policies.

Risk-Averse Facility Location for Green Closed-Loop Supply Chain Networks Design under Uncertainty

With the increasing attention given to environmentalism, designing a green closed-loop supply chain network has been recognized as an important issue. In this paper, we consider the facility location problem, in order to reduce the total costs and CO2 emissions under an uncertain demand and emission rate. Particularly, we are more interested in the risk-averse method for providing more reliable solutions. To do this, we employ a coherent risk measure, conditional value-at-risk, to represent the underlying risk of uncertain demand and CO2 emission rate. The resulting optimization problem is a 0-1 mixed integer bi-objective programming, which is challenging to solve. We develop an improved reformulation-linearization technique, based on decomposed piecewise McCormick envelopes, to generate lower bounds efficiently. We show that the proposed risk-averse model can generate a more reliable solution than the risk-neutral model, both in reducing penalty costs and CO2 emissions. Moreover, the proposed algorithm outperforms and classic reformulation-linearization technique in convergence rate and gaps. Numerical experiments based on random data and a ‘real’ case are performed to demonstrate the performance of the proposed model and algorithm.