Fuzzy Optimization and Decision Making最新文献

This paper proposes an uncertain mean-second order dominance model in the framework of uncertainty theory. By giving mean-expected utility equivalent, we show that the proposed model is suitable for rational and risk-averse investors because the portfolio produced by the model can give the investors the maximum expected return and in the meantime bring the investors expected utility value equal to or higher than the reference return no matter what specific utility functions the investors may take. By offering deterministic equivalents and comparing them with the uncertain mean-variance and uncertain mean-risk index models, we clarify the advantages of the proposed model, i.e., being easier to use and safer in investment. Furthermore, we give a numerical example and some experiments to illustrate the application of the model and the advantages of it.

Convertible bond is a hybrid financial derivative with the properties of debt and equity, which provides the holder with a right to convert bond into the issuer’s stock at a prescribed ratio in the future. This paper analyzes the valuation problems of convertible bond on the basis of uncertain fractional differential equation. Then the prices of convertible bond are obtained by means of expected value criterion and optimistic value criterion, respectively. Besides, numerical examples are given to compare expected value models with optimistic value models. Finally, an empirical study is provided to illustrate that the uncertain fractional stock model is superior to the classical stochastic model.

Carbon emissions trading is pivotal for advancing China’s low-carbon goals. As the primary tradable asset in the carbon market, carbon emission allowances inevitably experience price fluctuations. However, numerous empirical studies show that the frequency of real-world data is highly unstable, which results in the failure of probabilistic modeling. Therefore, this paper aims to model the dynamics of carbon emission allowance prices in China using four mainstream uncertain differential equations. The optimal model is chosen through rolling window cross-validation using the criterion of minimizing average testing errors. Parameters of the optimal model are determined by moment estimation based on residuals, and the model’s effectiveness is also assessed through uncertain two-sided hypothesis testing. Additionally, we forecast carbon emission allowance prices and their 95% confidence intervals for the next 14 business days. To manage trading risks, we propose a customized carbon option contract for pricing European carbon options and conduct sensitivity analysis on key parameters. Finally, we present a paradox of stochastic differential equations for modeling carbon emission allowance prices.

In order to rationally characterize the nondeterministic phenomena in queueing systems, there exist two mathematical systems, one is probability theory concerned with the analysis of random phenomena and the other is uncertainty theory concerned with the analysis of uncertain phenomena. Before using the above two mathematical systems to model the real queueing systems, we often need to face such a question, are the real queueing systems random or uncertain? In order to answer this question, we collect the arriving times of passengers from online car-hailing platform in Beijing, and then analyze the collected data based on stochastic renewal process and uncertain renewal process. Finally, by comparing samples and confidence intervals of the total numbers of passengers arriving on the online car-hailing platform under two mathematical systems, we come to the conclusion that the queueing systems in the real world are uncertain rather than random.

Since securities market is subject to a great deal of uncertainty and complexity, the return of securities cannot be accurately estimated by historical data. In this case, it must use experts’ knowledge and judgment. Therefore, we investigate portfolio selection problems in such uncertain environments. First, this paper regards the rate of return on security as an uncertain variable which obeys linear uncertainty distribution, and then provides the analytical expressions of the corresponding risk, return and risk index in the uncertain portfolio selection environment. Afterwards, we construct three types uncertain portfolio selection models with uncertain constraint, namely, the minimizing risk, the maximizing return and the maximizing belief degree. Meanwhile, in order to more intuitively reflect the investor’s sense of loss, three types uncertain portfolio selection models considering both uncertain constraint and risk index are also constructed. These models are transformed into corresponding deterministic models. Finally, through an example analysis, this paper obtains the portfolio selection strategies under different objectives, compares the results under different models, and analyzes the sensitivity of the parameters.

The shout option allows the investors to make "shouts" to the seller throughout the option’s duration. The investors’ payoff is higher between the intrinsic value at shout time and the intrinsic value at the maturity time. Previous shout option pricing is in the framework of probability theory. However, some unexpected events in real life can make the frequency deviate from the estimated distribution function, in which case we should use the uncertainty theory. This study investigates shout option pricing problems under uncertainty theory. It also derives pricing formulas for shout-call and shout-put options. Additionally, we design a numerical algorithm to compute the price of the shout options. Finally, this study applies the concept of the shout option to Microsoft’s stock data and examines the relationship between the option price and crucial parameters.

This study concentrates on the pricing issue in a low-carbon dual-channel (DC) supply chain, where the upper-level manufacturer is regulated by the cap-and-trade (CAT) mechanisms. Market demand is a key factor affecting pricing decision and demand uncertainty complicates the pricing problem. To deal with the challenge that only partial demand distribution information is available, this paper proposes a novel ambiguity distribution set to depict the uncertain demand. Under the proposed ambiguity distribution set, a robust fuzzy bi-level optimization pricing model is developed for the low-carbon DC supply chain. Three CAT regulation mechanisms, no CAT regulation, grandfathering (GF) mechanism and benchmarking (BM) mechanism, are considered to address the manufacturer’s CAT regulation. The analytically tractable counterpart of the proposed model is derived and the corresponding robust equilibrium solutions are obtained under three CAT mechanisms. Numerical analyses are carried out to explore the impact of the demand uncertainty on the manufacturer’s selection of the CAT regulation mechanism. The numerical results indicate that the uncertainty degree can change the manufacturer’s selection of the regulated mechanisms. Specifically, when the uncertainty degree is smaller, the BM mechanism is beneficial for the manufacturer comparing with the GF mechanism; when the uncertainty degree is bigger, the manufacturer prefers to GF mechanism rather than BM mechanism.

It has become a consensus in the international community to actively address global climate change issues and strive to achieve carbon reduction. For this purpose, carbon finance market plays a significant role in reducing carbon emissions by providing financial mechanisms to support and incentivize emission reduction projects. As a type of carbon finance derivative, carbon swap is an agreement between two parties whereby a floating price is exchange for a fixed price for carbon emission right over a specified period. How to price carbon swap before signing, i.e., determine the fixed price in the swap contract, and valuate carbon swap during the life of the swap contract are key issues. Noting the fact that the underlying asset of carbon swap is carbon price, the primary task is to model carbon price reasonably. Due to the inherent challenges and uncertainties associated with pricing carbon, frequency stability is often not guaranteed, resulting in the failure of probability based methods. Thus, this paper characterizes the carbon price using uncertain differential equation under the framework of uncertainty theory, and derives swap pricing and valuation formulas. Estimations for unknown parameters in the proposed model are given. Finally, with carbon spot price in European Energy Exchange, real data analyses are documented to illustrate our proposed methods in details.

This paper initializes higher-order uncertain calculus that deals with higher-order differentiation and multiple integration of uncertain process based on uncertainty theory. Fubini theorem and fundamental theorem of higher-order uncertain calculus are derived. Finally, this paper rigorously defines higher-order uncertain differential equations and introduces some analytic methods for solving these equations.

Uncertain nonlinear time series analysis is a set of statistical techniques that use uncertainty theory to predict future values via nonlinear dynamics based on the previous observations. By assuming that the disturbance term is an uncertain variable, an uncertain nonlinear time series model is derived in this paper. In addition, this paper presents a method to estimate unknown parameters in an uncertain nonlinear time series model. Finally, some real examples (motion analysis and epidemic spreading) are provided to illustrate uncertain nonlinear time series analysis. As a result, it is shown that the uncertain nonlinear time series model may provide higher forecast accuracy than linear one.