The Evaluation of Alternative Risk Control Schemes Based on Cumulative Prospect Theory

Based on the analysis of the evaluation problems associated with the risk control scheme for major engineering projects,the evaluation method of the risk control scheme considering the irrational behavior of evaluation members in fuzzy random environment is proposed.Firstly,a maximum entropy model corresponding to any evaluation member is es-tablished by using triangular fuzzy random variables and grey correlation coefficient in order to obtain the weight of each risk factor of the member.Secondly,a nonlinear programming model is established according to the principle of minimiz-ing deviation to estimate the weight of different evaluation members on the evaluation of alternative risk control schemes.Lastly,the cumulative entropy model is used to calculate the weight of risk control schemes.Cumulative prospect theory obtains the comprehensive prospect utility value of each alternative to determine the optimal alternative.

Robust user equilibrium model based on cumulative prospect theory under distribution-free travel time

The assumption widely used in the user equilibrium model for stochastic network was that the probability distributions of the travel time were known explicitly by travelers. However, this distribution may be unavailable in reality. By relaxing the restrictive assumption, a robust user equilibrium model based on cumulative prospect theory under distribution-free travel time was presented. In the absence of the cumulative distribution function of the travel time, the exact cumulative prospect value(CPV) for each route cannot be obtained. However, the upper and lower bounds on the CPV can be calculated by probability inequalities.Travelers were assumed to choose the routes with the best worst-case CPVs. The proposed model was formulated as a variational inequality problem and solved via a heuristic solution algorithm. A numerical example was also provided to illustrate the application of the proposed model and the efficiency of the solution algorithm.

Traffic assignment problem under tradable credit scheme in a bi-modal stochastic transportation network: A cumulative prospect theory approach

The traffic equilibrium assignment problem under tradable credit scheme(TCS) in a bi-modal stochastic transportation network is investigated in this paper. To describe traveler’s risk-taking behaviors under uncertainty, the cumulative prospect theory(CPT) is adopted. Travelers are assumed to choose the paths with the minimum perceived generalized path costs, consisting of time prospect value(PV) and monetary cost. At equilibrium with a given TCS, the endogenous reference points and credit price remain constant, and are consistent with the equilibrium flow pattern and the corresponding travel time distributions of road sub-network. To describe such an equilibrium state, the CPT-based stochastic user equilibrium(SUE) conditions can be formulated under TCS. An equivalent variational inequality(VI) model embedding a parameterized fixed point(FP) model is then established, with its properties analyzed theoretically. A heuristic solution algorithm is developed to solve the model, which contains two-layer iterations. The outer iteration is a bisection-based contraction method to find the equilibrium credit price, and the inner iteration is essentially the method of successive averages(MSA) to determine the corresponding CPT-based SUE network flow pattern. Numerical experiments are provided to validate the model and algorithm.

Cumulative prospect theory-based user equilibrium model with stochastic perception errors

The cumulative prospect theory(CPT) is applied to study travelers' route choice behavior in a degradable transport network. A cumulative prospect theory-based user equilibrium(CPT-UE) model considering stochastic perception error(SPE) within travelers' route choice decision process is developed. The SPE is conditionally dependent on the actual travel time distribution, which is different from the deterministic perception error used in the traditional logit-based stochastic user equilibrium. The CPT-UE model is formulated as a variational inequality problem and solved by a heuristic solution algorithm. Numerical examples are provided to illustrate the application of the proposed model and efficiency of the solution algorithm. The effects of SPE on the reference point determination, cumulative prospect value estimation, route choice decision and network performance evaluation are investigated.

Multi-Objective Optimization of Urban Bus Network Using Cumulative Prospect Theory

Multi-objective optimization of urban bus network can help improve operation efficiency of the transit system and develop strategies for reducing urban traffic congestion in China. The work used cumulative prospect theory, currently the most influential model for decision under uncertainty,to optimize urban bus network. To achieve the research objective, the work developed the theoretical framework of urban bus network optimization, including optimization principle, optimization objectives and constraints. Furthermore, optimization objectives could comprehensively reflect expectations of passengers and bus companies from the dimension of time, space and value. It is more scientific and reasonable compared with only one stakeholder or dimension alone in the previous studies. In addition,the technique for order preference by similarity to ideal solution(TOPSIS) was used to determine the positive and negative ideal alternative. The correlations between the optimization alternatives and the ideal alternatives were estimated by grey relational analysis simultaneously. The cumulative prospect theory(CPT) was used to determine the best alternative by comparing comprehensive prospect value of every alternative, accurately describing decision-making behavior compared with expected utility theory in actual life. Finally, Case of Xi'an showed that the method can better adjust the bus network,and the optimization solution is more reasonable to meet the actual needs.

The Park-and-Ride Behavior in a Cumulative Prospect Theory-Based Model

As an effective travel demand management means,park-and-ride(P&R)mode is an important part of urban traffic.In a traffic corridor with P&R service,suppose that the travel time on highway is uncertain,a cumulative prospect theory(CPT)-based travel decision-making model is established with two travel modes of driving all the way and(P&R).With this setting,the effect of various factors such as the transit fare rate,the parking fee and the total travel demand on the CPT-based and expected utility theory(EUT)-based equilibrium results are compared.In addition,the sensitivity analysis focus on CPT-related parameters are also performed.The numerical results in our case show that the equilibrium flow on P&R mode is always underestimated in an EUT-based model,especially for a low total travel demand.Also,it is found that reducing the transit fare rate or parking fee for P&R station and raising the parking fee for CBD has the same effect on promoting more commuters transfer to P&R mode,whatever CPT-based or EUT-based model is employed.Furthermore,commuter’s reference dependence characteristic is also observed in a CPT-based model,and it is especially noticeable when the road uncertainty is large.

A New Method of Portfolio Optimization Under Cumulative Prospect Theory

In this paper, the portfolio selection problem under Cumulative Prospect Theory （CPT） is investigated and a model of portfolio optimization is presented. This model is solved by coupling scenario generation techniques with a genetic algorithm. Moreover, an Adaptive Real-Coded Genetic Algorithm （ARCGA） is developed to find the optimal solution for the proposed model. Computational results show that the proposed method solves the portfolio selection model and that ARCGA is an effective and stable algorithm. We compare the portfolio choices of CPT investors based on various bootstrap techniques for scenario generation and empirically examine the effect of reference points on investment behavior.

A stochastic user equilibrium model solving overlapping path and perfectly rational issues

Traffic assignment has been recognized as one of the key technologies in supporting transportation planning and operations.To better address the perfectly rational issue of the expected utility theory(EUT)and the overlapping path issue of the multinomial logit(MNL)model that are involved in the traffic assignment process,this paper proposes a cumulative prospect value(CPV)-based generalized nested logit(GNL)stochastic user equilibrium(SUE)model.The proposed model uses CPV to replace the utility value as the path performance within the GNL model framework.An equivalent mathematical model is provided for the proposed CPV-based GNL SUE model,which is solved by the method of successive averages(MSA).The existence and equivalence of the solution are also proved for the equivalent model.To demonstrate the performance of the proposed CPV-based GNL SUE model,three road networks are selected in the empirical test.The results show that the proposed model can jointly deal with the perfectly rational issue and the overlapping path issue,and additionally,the proposed model is shown to be applicable for large road networks.

Travel Decision Model of Heterogeneous Commuters under Uncertain Environment

In order to better describe the commuter's travel decision-making behavior under different travel environment,heterogeneous commuters and types are defined,and the commuters are divided into three types,including conservative type,neutral type and adventure type,respectively,analysis on the travel environment supply and the travel environment demand.Suppose the travel demand obeys the gamma distribution and the capacity obeys the beta distribution,and the travel time function of different commuter type is deduced,the travel decision model based on the cumulative foreground theory is established.Analyze the example results,compared with the fluctuation of travel demand,the degradation of traffic capacity has a more significant impact on travel decision-making behavior;and different types of commuters cause different disturbances to travel decision-making behavior.

A Method for Risky Multiple Attribute Decision Making with Four - dimensional Reference Point

A method based on cumulative prospect theory was proposed to solve risky multiple attribute decision making problems with Four -dimensional reference points. Considering the influence of different learning processes and corresponding features on decision-making, a new reference-learning behavior is added, and a risk-based multiple-attribute decision-making method based on four-dimensional reference point cumulative prospect theory is proposed. Firstly, according to the cumulative prospect theory, the prospect value and the decision function value of the four reference points of learning, time, evaluation value and expected value are calculated respectively, and the cumulative prospect value matrix of each program dynamic is formed. Secondly,according to the WAA operalor, Maximize the stage weighting model to obtain the integrated cumulative prospect value. Finally, on the basis of this, the alternatives are sorted according to the size of the total cumulative prospect value, and compared with other methods, the validity and scientific of the proposed method are proved.

Behavioral Portfolio Selection with Loss Control

In this paper we formulate a continuous-time behavioral （4 la cumulative prospect theory） portfolio selection model where the losses are constrained by a pre-specified upper bound. Economically the model is motivated by the previously proved fact that the losses Occurring in a bad state of the world can be catastrophic for an unconstrained model. Mathematically solving the model boils down to solving a concave Choquet minimization problem with an additional upper bound. We derive the optimal solution explicitly for such a loss control model. The optimal terminal wealth profile is in general characterized by three pieces： the agent has gains in the good states of the world, gets a moderate, endogenously constant loss in the intermediate states, and suffers the maximal loss （which is the given bound for losses） in the bad states. Examples are given to illustrate the general results.