Fractional Order Stochastic Differential Equation with Application in European Option Pricing

Memory effect is an important phenomenon in financial systems, and a number of research works have been carried out to study the long memory in the financial markets. In recent years, fractional order ordinary differential equation is used as an effective instrument for describing the memory effect in complex systems. In this paper, we establish a fractional order stochastic differential equation (FSDE) model to describe the effect of trend memory in financial pricing. We, then, derive a European option pricing formula based on the FSDE model and prove the existence of the trend memory (i.e., the mean value function) in the option pricing formula when the Hurst index is between 0.5 and 1. In addition, we make a comparison analysis between our proposed model, the classic Black-Scholes model, and the stochastic model with fractional Brownian motion. Numerical results suggest that our model leads to more accurate and lower standard deviation in the empirical study

Dynamic Hedging Based on Fractional Order Stochastic Model with Memory Effect

Many researchers have established various hedge models to get the optimal hedge ratio. However, most of the hedge models only discuss the discrete-time processes. In this paper, we construct the minimum variance model for the estimation of the optimal hedge ratio based on the stochastic differential equation. At the same time, also by considering memory effects, we establish the continuous-time hedge model with memory based on the fractional order stochastic differential equation driven by a fractional Brownian motion to estimate the optimal dynamic hedge ratio. In addition, we carry on the empirical analysis to examine the effectiveness of our proposed hedge models from both in-sample test and out-of-sample test

Molecular Mechanism Underlying the Interaction of Typical Sac10b Family Proteins with DNA

The Sac10b protein family is regarded as a family of DNA-binding proteins that is highly conserved and widely distributed within the archaea. Sac10b family members are typically small basic dimeric proteins that bind to DNA with cooperativity and no sequence specificity and are capable of constraining DNA negative supercoils, protecting DNA from Dnase I digestion, and do not compact DNA obviously. However, a detailed understanding of the structural basis of the interaction of Sac10b family proteins with DNA is still lacking. Here, we determined the crystal structure of Mth10b, an atypical member of the Sac10b family from Methanobacterium thermoautotrophicum ΔH, at 2.2 Å. Unlike typical Sac10b family proteins, Mth10b is an acidic protein and binds to neither DNA nor RNA. The overall structure of Mth10b displays high similarity to its homologs, but three pairs of conserved positively charged residues located at the presumed DNA-binding surface are substituted by non-charged residues in Mth10b. Through amino acids interchanges, the DNA-binding ability of Mth10b was restored successfully, whereas the DNA-binding ability of Sso10b, a typical Sac10b family member, was weakened greatly. Based on these results, we propose a model describing the molecular mechanism underlying the interactions of typical Sac10b family proteins with DNA that explains all the characteristics of the interactions between typical Sac10b family members and DNA

Design Method and Verification of Electroosmosis-Vacuum Preloading Method for Sand-Interlayered Soft Foundation

The design method of electroosmosis-vacuum preloading for soft foundation treatment is not systematic and complete, thereby restricting the application of the technology in engineering. A design method for the electroosmosis-vacuum preloading treatment of sand-interlayered soft foundation is therefore presented. A compressible electrical prefabricated vertical drain is developed, and a vacuum sealing and draining system is designed for the application of the electroosmosis-vacuum preloading in sand-interlayered soft foundation. Calculation formulas of site resistance considering the interlayer and interface resistivity of the electrode are established to design the power supply and electrical circuit. A simple numerical simulation method is proposed to predict the ground settlement treated by electroosmosis-vacuum preloading. A field test of electroosmosis-vacuum preloading is designed using the suggested method, and comparison tests between the electroosmosis-vacuum preloading and the vacuum preloading are performed to verify the proposed technique. The test results show that the proposed design method is reasonable for the design of electroosmosis-vacuum preloading in engineering

The Optimization of Working Time for a Consecutively Connected Production Line

Most factory production processes are completed by machines and workers on production lines. The operation schedule is arranged to reduce the cost of the enterprises to obtain the maximum economic profit for sustainable running. Previous studies usually investigated the working time while only considering the workers’ conditions. This study proposed a method to optimize the operation schedule by jointly considering the workers’ fatigue states and the operation states of machines. This method was proposed based on a system structure called the multistate consecutively connected system (MCCS), which has been widely applied in many areas, such as electronic communications. This structure is also an analogy of the production line. The corresponding model is constructed based on the universal generating function (UGF) since it is a powerful tool in modeling a consecutively connected system. The proposed model can be used to evaluate the different productivities of different types of workers in different states and to realize the screening of the whole scheme through simulation. According to the proposed method, we obtained the optimal operation schedule, including the working time, rest time and allocation strategy for a production line system. Some examples are provided to illustrate the proposed method

Applying Big Data Analytics to Monitor Tourist Flow for the Scenic Area Operation Management

Considering the rapid development of the tourist leisure industry and the surge of tourist quantity, insufficient information regarding tourists has placed tremendous pressure on traffic in scenic areas. In this paper, the author uses the Big Data technology and Call Detail Record (CDR) data with the mobile phone real-time location information to monitor the tourist flow and analyse the travel behaviour of tourists in scenic areas. By collecting CDR data and implementing a modelling analysis of the data to simultaneously reflect the distribution of tourist hot spots in Beijing, tourist locations, tourist origins, tourist movements, resident information, and other data, the results provide big data support for alleviating traffic pressure at tourist attractions and tourist routes in the city and rationally allocating traffic resources. The analysis shows that the big data analysis method based on the CDR data of mobile phones can provide real-time information about tourist behaviours in a timely and effective manner. This information can be applied for the operation management of scenic areas and can provide real-time big data support for “smart tourism”

Functional Relevance of Interleukin-1 Receptor Inter-domain Flexibility for Cytokine Binding and Signaling

The interleukin 1 (IL-1) receptor family, whose members contain three immunoglobulin-like domains (D1-D3) in the extracellular region, is responsible for transmitting pleiotropic signals of IL-1 cytokines. The inter-domain flexibility of IL-1 receptors and its functional roles have not been fully elucidated. In this study, we used small-angle X-ray scattering to show that ligand-binding primary receptors and co-receptors in the family all have inherent inter-domain flexibility due to the D2/D3 linker. Variants of the IL-1RAcP and IL-18Rβ co-receptors with mutated D2/D3 linkers cannot form a cytokine-receptor complex and mediate signaling. Our analysis further revealed that these mutated co-receptors exhibited a changed conformational ensemble, suggesting that loss of function is due to the alteration of receptor dynamics. Taken together, our results demonstrate that the D2/D3 linker is a critical functional determinant of IL-1 receptor and underscore the important roles of the inter-domain flexibility in cytokine/receptor binding and signaling

Excess Mcm2-7 license dormant origins of replication that can be used under conditions of replicative stress

In late mitosis and early G1, replication origins are licensed for subsequent use by loading complexes of the minichromosome maintenance proteins 2-7 (Mcm2-7). The number of Mcm2-7 complexes loaded onto DNA greatly exceeds the number of replication origins used during S phase, but the function of the excess Mcm2-7 is unknown. Using Xenopus laevis egg extracts, we show that these excess Mcm2-7 complexes license additional dormant origins that do not fire during unperturbed S phases because of suppression by a caffeine-sensitive checkpoint pathway. Use of these additional origins can allow complete genome replication in the presence of replication inhibitors. These results suggest that metazoan replication origins are actually comprised of several candidate origins, most of which normally remain dormant unless cells experience replicative stress. Consistent with this model, using Caenorhabditis elegans, we show that partial RNAi-based knockdown of MCMs that has no observable effect under normal conditions causes lethality upon treatment with low, otherwise nontoxic, levels of the replication inhibitor hydroxyurea