Research On Modeling,Analysis And Related Application Based On Cumulative Prospect Theory

This paper studies the application of prospect theory(PT)and cumulative prospect theory(CPT).We studied what kind of impact of lossaverse consumers on market demand under Kahahm and Tversky’s prospect theory,and explored the relationship between loss-averse consumers with a single factor reference point and market demand sensitivity.Further,we studied the impact of loss-averse consumers with dual-factor reference points on market demand.Finally,we presented the relationship between loss-averse consumers with a single factor reference point and market demand sensitivity,where consumers are divided into low reference point consumers and high reference point consumers.This paper showed that in the case of a single reference point,the relationship between loss-averse consumers and market demand sensitivity is related to consumers’ cumulative distribution functions for product valuation.In the case of dual-factor reference points,the impact of loss-averse consumers on market demand is related to the range of the product price and the relative size of the dual-factor reference points.In the case of the two types of consumers with a single factor reference point,loss-averse consumers may lead to market demand more responsive to losses or gains.We argue that the distribution function of psychological valuation is related.However,loss-averse consumers directly affect the sensitivity of local market demand.This finding has certain significance for studying product pricing and market demand.Finally,we formulated the M/M/1 model featuring a reference point in wealth,S-shape utility functions with loss aversion,and a probability weighting function under Kahahm and Tversky’s cumulative prospect theory.It highlighted the well-posedness issue of the model and analyzed the optimal arrival rate of customers.The results showed that the higher the rate at which the firm can process orders,the higher the rate at which customers will place orders.The impact of commodity prices and customers’ marginal waiting costs is opposite to the service revenue on the optimal arrival rate under CPT.As a comparison,it presented the M/M/1 model under expected utility theory(EU),where the influence of each factor on the optimal queuing rate is easy to analyze because the utility function is globally concave.In the numerical case,the results of CPT and EU are similar,but the optimal customer arrival rate calculated by CPT is always lower than that under EU.