Fuzzy Price Research Articles

An Inventory Model for Deteriorating Items with Price Dependent Demand Under Fuzzy and Neutrosophic Fuzzy Environment

This paper represents an inventory model of deteriorating items under fuzzy and neutrosophic environment without allowing shortages in inventory. Demand is price dependent and is compared between crisp, fuzzy and neutrosophic fuzzy demand. Realistically it is observed that although the cycle time of any supply chain system is uncertain but uncertainty is mainly dependent on the selling price. So, here we have compared the model using crisp, fuzzy and neutrosophic fuzzy demand. The result is illustrated with the help of numerical example under fuzzy and neutrosophic fuzzy demand. KEYWORDS: Inventory, Fuzzy and Neutrosophic Fuzzy Price dependent Demand.

Price estimation based on business model pricing strategy and fuzzy logic

Pricing, as one of the most important aspects of a business, should be taken seriously. Whatever affects a company's pricing system tends to affect its profits and losses as wall. Currently, many manufacturing companies fix product prices manually by member of an organization's management team. However, due to the imperfect nature of humans, an extremely low or high price may be fixed, which is detrimental to the company in either case. This paper proposes the developement of a fuzzy-based price expert system (Expert Fuzzy Price (EFP)) for manufacturing companies. This system will be able to recommend appropriate prices for products in manufacturing companies based on four major pricing strategic goals, namely : Product Demand, Price Skimming, Competition Price, and Target population.

Application of fuzzy Malliavin calculus in hedging fixed strike lookback option

<abstract><p>In this paper, we develop a Malliavin calculus approach for hedging a fixed strike lookback option in fuzzy space. Due to the uncertainty in financial markets, it is not accurate to describe the problems of option pricing and hedging in terms of randomness alone. We consider a fuzzy pricing model by introducing a fuzzy stochastic differential equation with Skorohod sense. In this way, our model simultaneously involves randomness and fuzziness. A well-known hedging strategy for vanilla options is so-called $ \Delta $-hedging, which is usually derived from the Itô formula and some properties of partial differentiable equations. However, when dealing with some complex path-dependent options (such as lookback options), the major challenge is that the payoff function of these options may not be smooth, resulting in the estimates are computationally expensive. With the help of the Malliavin derivative and the Clark-Ocone formula, the difficulty will be readily solved, and it is also possible to apply this hedging strategy to fuzzy space. To obtain the explicit expression of the fuzzy hedging portfolio for lookback options, we adopt the Esscher transform and reflection principle techniques, which are beneficial to the calculation of the conditional expectation of fuzzy random variables and the payoff function with extremum, respectively. Some numerical examples are performed to analyze the sensitivity of the fuzzy hedging portfolio concerning model parameters and give the permissible range of the expected hedging portfolio of lookback options with uncertainty by a financial investor's subjective judgment.</p></abstract>

Design of red chili commodity pricing using the BPMN approach and Sugeno's fuzzy inference system

Red chili is Indonesia's leading commodity. Red chili is a raw material for various food products, cosmetics, pharmaceuticals and others. Fluctuations in the availability of red chili commodity supply affect the price of red chili commodity products. Pricing can occur because of supply and demand. Un­cer­tain conditions also influence pricing due to fluctuations in raw material prices, ultimately affecting the price of carrageenan products. This condition makes price determination very difficult. Therefore, this study aims to analyze and design a pricing mechanism and determine the optimal margin in the red chili commodity marketing system. This study uses a systems analysis and design approach. Input-process-output (IPO) diagrams describe system requirements. Industrial business processes are described by the Business Process Model and Notation (BPMN) ver. 16.0. Meanwhile, to determine the optimal margin, Sugeno's fuzzy inference system approach is used by simulating the model in 3 margin scenarios: pessimistic, moderate, and optimistic. The simulation results were tested using the MAPE test, in which the results were compared between fuzzy price results and markup prices using markup values of 20%, 25%, and 30%. The analysis results show that the price is determined by demand and supply. The price obtained from the formulation of the Sugeno fuzzy model shows an optimal margin of Rp. 16,600.

N-Fold Compound Option Fuzzy Pricing Based on the Fractional Brownian Motion

N-Fold Compound Option Fuzzy Pricing Based on the Fractional Brownian Motion

Credit risk pricing under fuzzy mixed fractional Brownian motion

In order to introduce the long term memory of financal markets and fuzziness to the study of credit risk pricing, this paper develops a new framework by using fuzzy mixed Brownian motion to describe the motion of the underlying assets and deduces a new credit risk fuzzy pricing formula. The influence of the long-term momery and fuzziness is emphatically analyzed. Finally, for better understanding, this study provides an example of triangular fuzzy numbers to compare the price given by different models. The results show that the credit risk model under fuzzy mixed fractional Brownian motion given in this paper is more consistent with the financial market.

Pricing of satellite image data products: Neutrosophic fuzzy pricing approaches under different game scenarios

With the gradual commercialization of satellite image data products, their pricing decisions become an important link for providers to achieve profits. This study aims to investigate the pricing problems of data products in a neutrosophic fuzzy environment. A main contribution is that two game scenarios, including the Bertrand and Stackelberg game scenarios, are discussed by considering the specific features of satellite image data products (SIDPs) market. Two main SIDPs providers are regarded as two players in the game. The innovation is that the concept of neutrosophic fuzzy variables is presented to fully express the uncertainty existing in real-world problems. As a result, the truth, indeterminacy and falsity degrees of decision makers for some problem parameters can determined in an intuitive and convenient fashion. Additionally, the expected value of neutrosophic variables is defined to facilitate the establishment of pricing models. After some equilibrium formulas are derived, a numerical example is provided to obtain the optimal pricing and expected profits. The effects of different power structures of providers are also analyzed and some interesting conclusions are made. Last, the advantages of our methods are demonstrated through comparative analyses. Furthermore, sensitivity analyses are conducted to identify the influence of important problem parameters and weight coefficients on final pricing decisions. The results demonstrate that the proposed approaches are feasible and can provide guidelines for the pricing of satellite image data products.

The effect of international energy market shocks on coal price of China based on the fuzzy integrated vector auto regressive and error correction model

From the perspective of external market shocks, this paper proposed fuzzy integrated vector auto regression (FVAR) model that determines the long-term basis and short-term basis interactions of China’s coal price with international energy prices. The proposed FVAR preform coal price fluctuation based on long-term and short term span in six stages including unit root testing, Johansen cointegration test, vector auto regression (VAR) model construction, fuzzification of VAR model, vector error correction (VEC) model and an impulse response function(IRF). It is observed that there is a steady long-term stability and equilibrium bond between the China’s domestic coal price, international coal price and the international crude (unrefined) oil price. The international coal and international crude oil price have an opposite effect on China’s domestic coal price. In addition, the former has a stronger fuzzy price discovery function on China’s domestic coal market than the latter. In the short term, China’s domestic coal price is more complex to instability reactions and is affected by market expectations. The international energy market is more effective than domestic coal market, and there is a relatively stable price adjustment mechanism between the two, with the international coal price playing a leading role in the fuzzy guidance of China’s coal price. Therefore, in reference to international energy pricing models, the paper proposes a fuzzy pricing model for a coal futures index based on the coal futures trading price and supplemented by the premium and discount agreed to by both trading parties.

Pricing European Option Under Fuzzy Mixed Fractional Brownian Motion Model with Jumps

As we all know, the financial environment on which option prices depend is very complex and fuzzy, which is mainly affected by the risk preferences of investors, economic policies, markets and other non-random uncertainty. Thus, the input data in the options pricing formula cannot be expected to be precise. However, fuzzy set theory has been introduced as a main method for modeling the uncertainties of the input parameters in the option pricing model. In this paper, we discuss the pricing problem of European options under the fuzzy environment. Specifically, to capture the features of long memory and jump behaviour in financial assets, we propose a fuzzy mixed fractional Brownian motion model with jumps. Subsequently, we present the fuzzy prices of European options under the assumption that the underlying stock price, the risk-free interest rate, the volatility, the jump intensity and the mean value and variance of jump magnitudes are all fuzzy numbers. This assumption allows the financial investors to pick any option price with an acceptable belief degree to make investment decisions based on their risk preferences. In order to obtain the belief degree, the interpolation search algorithm has been proposed. Numerical analysis and examples are also presented to illustrate the performance of our proposed model and the designed algorithm. Finally, empirically studies are performed by utilizing the underlying SSE 50 ETF returns and European options written on SSE 50 ETF. The empirical results indicate that the proposed pricing model is reasonable and can be treated as a reference pricing tool for financial analysts or investors.

Fuzzy pricing of binary option based on the long memory property of financial markets

Fuzzy pricing of binary option based on the long memory property of financial markets

An Incremental-Hybrid-Yager’s Entropy Model for Dynamic Portfolio Selection with Fuzzy Variable

To settle down the resolutional uncertainty in optimum portfolio strategy, this paper addresses an incremental-hybrid-Yager’s entropy model to newly describe the relationship between return and risk. Different from the traditional multiperiod portfolio, we design the ratio threshold to divide asset price into different time interval and use state instead of time point to model the dynamic portfolio process. In addition, fuzzy variables are utilized to represent prices of assets, while historical data based on Markov chain is exploited to estimate membership functions of fuzzy prices. At last, a compromised genetic algorithm is designed, and the numerical example shows that the proposed model achieves solid returns compared against the mean-variance model and Markov chain Monte Carlo method.

EPC renewable project evaluation: a fuzzy real option pricing model

ABSTRACTEngineer–procure–construct (EPC) projects in the renewable energy field have attracted considerable attention and have become a hot spot of investment because of their management advantages and supportive policies. However, the investment value of EPC projects is difficult to evaluate when considering the uncertainty factors and non-preciseness of input data, which are often neglected by traditional valuation methodology. Therefore, a fuzzy real option pricing model, which can do away with the vagueness of project data, could be a useful approach in evaluating the investment value of EPC projects. Based on the Black–Scholes formula and fuzzy theory, the authors propose a fuzzy real option pricing model that introduces a fuzzy number (T-number) to describe uncertainty factors, and the optimal investment decision criterion is also described to calculate the optimal investment timing. Lastly, a data set of a real EPC project as an illustrative example of valuation is presented, and the results based on the proposed model are satisfactory.

Forward and reverse flows pricing decisions for two competing supply chains with common collection centers in an intuitionistic fuzzy environment

This paper studies the selling and the acquisition price decisions for the products of two partially overlapping competing supply chains in an intuitionistic fuzzy environment. In the forward flows, the supply chains are assumed to produce substitutable products and sell them in a duopoly marketplace. The reverse flows are also concentrated on collecting and recycling the used products. While regularly it is assumed that the structures of the competing supply chains are completely separated, this paper assumes that the supply chains benefit from the services of the same collection centers. Considering the collection centers and the two supply chains to act as three integrated entities having enough bargaining powers to affect the decisions of each other, this paper concentrates on investigating the effects of different power structure scenarios on the optimal pricing decisions made by all of the parties involved in the problem. Another important feature of this study is that it employs the concept of intuitionistic fuzzy sets to integrate uncertainties and impressions inevitable in real-world situations into the decision-making process. To achieve this purpose, first, a new credibility-based definition for the concept of intuitionistic fuzzy variables is provided. This concept is then employed in the process of developing the intuitionistic fuzzy pricing models. A new expected value operator is also defined which is employed to transform the credibility-based intuitionistic fuzzy programming problems into their crisp equivalents. A numerical example is employed to discuss the properties of the introduced concepts, providing some interesting managerial implications regarding the defined problem.

A fuzzy pricing model for a green competitive closed-loop supply chain network design in the presence of disruptions

Abstract This paper presents a fuzzy bi-objective bi-level model with a price-dependent demand for the network design of a closed-loop supply chain in the presences of random disruptions at suppliers. The environmental issues resulted in considering two strategies, namely: adding a reverse flow to the supply chain and controlling the amount of CO2 emissions. In this model, the uncertain demand is assumed as a function of price offered to the customers by the supply chain and its rival. The proposed model determines outsourcing strategies, pricing decisions that maximize the total profit in such a competitive situation and minimizes the amount of CO2 emissions by production processes. A hybrid approach combining Karush–Kuhn–Tucker (K-K-T) conditions and possibilistic method was developed to solve the fuzzy bi-level model. Then the e-constraint method is used to convert the integrated bi-objective model to a single-objective one. Finally, important managerial insights are obtained from an empirical case study of a filter industry.

Pricing, collection, and effort decisions with coordination contracts in a fuzzy, three-level closed-loop supply chain

In this paper, a fuzzy, closed-loop supply chain (CLSC), with one manufacturer, one retailer and one collector, is investigated. The optimal decision problem is analyzed based on a fuzzy price and sales effort-dependent demand to evaluate how members decide wholesale price, collection rate, retail price, and sales effort under different decision-making structures. Six game theory models are established and optimal solutions are extracted and compared by applying game and fuzzy theories. According to the results, collaboration between a manufacturer and retailer is favorable for both customers and the chain as a whole; the most effective model for collecting used products is collaboration between the manufacturer and collector. Finally, a practical, new channel coordination scheme is explored to match the performance of a decentralized CLSC to that of a centralized CLSC. The results illustrate that the proposed contract can effectively coordinate decentralized CLSCs. It is also beneficial from both consumer and environmental perspectives.

Fuzzy stochastic price scenario based portfolio selection and its application to BSE using genetic algorithm

This paper is concerned with portfolio selection problem using a fuzzy stochastic price scenario. In this scenario, a ratio factor (k) is calculated from the historical data to generated the future price of the stocks of Bombay Stock Exchange. The ratio factor k of different stocks are treated as a fuzzy numbers, which in turn gives future fuzzy prices of the stocks. Returns on the stocks are calculated from the future price of the stocks. Rejection of the assets are done based on returns calculated from the worst case scenario. If the returns of an asset exceed the investor's risk tolerance then the asset are not included in the portfolio. The definition of capital budget has been reformed to include the transaction cost with the capital budget. This process is implemented in two stage multi-objective fuzzy probabilistic programming problem which is then solved using a fuzzy genetic algorithm to obtain maximum short term and long term returns. A case study of Bombay Stock Exchange is provided to illustrate the above model.

A geometric Levy model for [formula omitted]-fold compound option pricing in a fuzzy framework

In this paper, we study the problem of n-fold compound option valuation using the martingale method and the theory of fuzzy sets. We adopt a geometric Levy process for modeling the underlying asset price dynamics. The log-price is the sum of a Brownian motion with drift and a Poisson process describing jumps in the price. To obtain the pricing formula for n-fold compound option, we use the Esscher transformed martingale measure as the equivalent martingale measure. The major challenge in deriving the closed-form analytic expression for n-fold compound options is to calculate complex multivariate normal integrals; the complexity is due to the sophisticated structure of the options. In order to overcome this difficulty, we prove a mathematical expectation related to multivariate normal variables. To the best of our knowledge, this report describes the first time that such an approach has been adopted, and it is highly useful in the pricing of n-fold compound options and many other financial derivatives. Because the uncertainty in financial markets simultaneously involves randomness and fuzziness, we assume that the underlying asset price follows a fuzzy stochastic process. Under this assumption, the α-cut of the fuzzy price of n-fold compound call options is derived. Considering a decision maker’s subjective judgment, the permissible range of the expected prices of n-fold compound call options with uncertainty is given. Finally, numerical examples are presented to illustrate and analyze the theoretical results.

Dynamic pricing of excess capacity in production networks by fuzzy logic

The research concerns a make to order manufacturing environment and two classes of customers who submit orders: core customers (long-term partnership) and short-term customers. The orders submitted by the short-term customers depend on the price and service level proposed by the firm. This research proposes a pricing policy based on a fuzzy tool to set the price for short-term customers in production networks. The fuzzy tool captures the state of the manufacturing system in terms of workload of the manufacturing system, reliability and demand fluctuations. The fuzzy tool developed supports the cooperation mechanism among the enterprises of the production network. A discrete event simulation environment is used to test the proposed approach in a static and dynamic environment. The numerical results are compared to the case without cooperation among the firms within the production network. The simulation results show how the proposed approach outperforms the other policies in all conditions tested. The combination of fuzzy dynamic price and cooperation mechanism improves the performance with low movements of orders among the partners of the network; this means that the transportation costs have a low impact.

Pricing Geometric Asian Options Under Fuzzy Stochastic Environment

Due to the uncertainty in reality consists of randomness and fuzziness, we employ stochastic analysis and fuzzy set theory to explore the pricing of geometric Asian options. In the fuzzy stochastic world, the price of the underlying asset is assumed to follow a fuzzy stochastic process of which the classic pricing model is a special case. We derive the analytic fuzzy prices of geometric Asian options and their crisp values based on possibilistic mean. Numerical analysis shows that the degree of the fuzziness of the option prices is a increasing function in the degree of the fuzziness of the underlying price. Moreover, from the perspective of the possibilistic means of option prices, the investors are aversive to fuzziness and they ask compensation for fuzziness.

Fuzzy pricing of geometric Asian options and its algorithm

Owing to the fluctuations of the financial market, input data in the options pricing formula cannot be expected to be precise. This paper discusses the problem of pricing geometric Asian options under the fuzzy environment. We present the fuzzy price of the geometric Asian option under the assumption that the underlying stock price, the risk-free interest rate and the volatility are all fuzzy numbers. This assumption makes the financial investors to pick any geometric Asian option price with an acceptable belief degree. In order to obtain the belief degree, the interpolation search algorithm has been proposed. Some numerical examples are presented to illustrate the rationality and practicability of the model and the algorithm. Finally, an empirical study is performed based on the real data. The empirical study results indicate that the proposed fuzzy pricing model of geometric Asian option is a useful tool for modeling the imprecise problem in the real world.