Based on the generalized discrete Fourier transform, the generalized orthogonal discrete W transform and its fast algorithm are proposed and derived in this paper. The orthogonal discrete W transform proposed by Zhongde Wang has only four types. However, the generalized orthogonal discrete W transform proposed by us has infinite types and subsumes a family of symmetric transforms. The generalized orthogonal discrete W transform is a real-valued orthogonal transform, and the real-valued orthogonal transform of a real sequence has the advantages of simple operation and facilitated transmission and storage. The generalized orthogonal discrete W transforms provide more basis functions with new frequencies and phases and hence lead to more powerful analysis and processing tools for communication, signal processing, and numerical computing.

Jichao Sun

Zhengping Zhang

Generalized Orthogonal Discrete W Transform and Its Fast Algorithm

This paper investigates the pricing of discretely sampled variance swaps under a Markov regime-switching jump-diffusion model. The jump diffusion, as well as other parameters of the underlying stock&#x2019;s dynamics, is modulated by a Markov chain representing different states of the market. A semi-closed-form pricing formula is derived by applying the generalized Fourier transform method. The counterpart pricing formula for a variance swap with continuous sampling times is also derived and compared with the discrete price to show the improvement of accuracy in our solution. Moreover, a semi-Monte-Carlo simulation is also presented in comparison with the two semi-closed-form pricing formulas. Finally, the effect of incorporating jump and regime switching on the strike price is investigated via numerical analysis.

Shican Liu

Yu Yang

Hu Zhang

Yonghong Wu

Variance Swap Pricing under Markov-Modulated Jump-Diffusion Model

Based on the analysis of the shortage of emergency rescue services and the supervision of public-private-partnership (PPP) projects, this paper explores the rent-seeking game predicament and establishes a three-player rent-seeking game model among government regulators, private enterprises, and government agents in the bidding operation of PPP projects by learning from Stackelberg game theory. Through the numerical simulation analysis, this paper explores the impact of the relevant variables on the model results, which can lead to the following conclusions: the emphasis on government regulators changes due to rent-seeking cost changes; when the success rate of verification is high, government regulators can take supervision randomly. Inversely, supervision channels should be broadened when the supervision fails. When the punishment on government agents and private enterprises is great, relaxing supervision may be appropriate. This study proposes the relevant policy recommendations for government regulators to improve their work.

Guangxi Cao

Ling Zhou

The Optimal PPP Model of Emergency Rescue Service

Understanding the impact of heterogeneity on the evolution of group opinions can enlighten us on how to effectively organize, redesign, and improve decision-making efficiency. This article explores mainly the effects of heterogeneity on the evolution of group opinions. It is found that the heterogeneity of individuals&#x2019; openness has an important influence on the ability to aggregate group opinions. According to the average amount of clusters and Herfindahl&#x2013;Hirschman Index (HHI) under different network structures, heterogeneity often improves the ability. In addition, for the small-world network and random network, there is little difference in the aggregation ability from both the average amount of clusters and the Herfindahl&#x2013;Hirschman Index. While for the regular network, the ability is obviously weaker than that of the other two. This result also shows that the randomness of interaction between members will enhance the cohesion of a group.

An Lu

Haifeng Ling

Zhengping Ding

How Does the Heterogeneity of Members Affect the Evolution of Group Opinions?

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Discrete Dynamics in Nature and Society publishes research that links basic and applied research relating to discrete dynamics of complex systems encountered in the natural and social sciences.

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Chief Editor, Dr&nbsp;Renna, is an associate professor at the University of Basilicata, Italy. His research interests include manufacturing systems, production planning and enterprise networks.&nbsp;

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Discrete Dynamics in Nature and Society - Table of contents 2021

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Discrete Dynamics in Nature and Society