Pricing Catastrophe Options with Credit Risk in a Regime-Switching Model

In this paper,we consider the price of catastrophe options with credit risk in a regime-switching model.We assume that the macroeconomic states are described by a continuous-time Markov chain with a finite state space.By using the measure change technique,we derive the price expressions of catastrophe put options.Moreover,we conduct some numerical analysis to demonstrate how the parameters of the model affect the price of the catastrophe put option.

Hyper Catastrophe on 4-Dimensional Canards

When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.

The role of AFAP1-AS1 in mitotic catastrophe and metastasis of triple-negative breast cancer cells by activating the PLK1 signaling pathway

Triple-negative breast cancer(TNBC)is characterized by fast growth,high metastasis,high invasion,and a lack of therapeutic targets.Mitosis and metastasis of TNBC cells are two important biological behaviors in TNBC malignant progression.It is well known that the long noncoding RNA AFAP1-AS1 plays a crucial role in various tumors,but whether AFAP1-AS1 is involved in the mitosis of TNBC cells remains unknown.In this study,we investigated the functional mechanism of AFAP1-AS1 in targeting Polo-like Kinase 1(PLK1)activation and participating in mitosis of TNBC cells.We detected the expression of AFAP1-AS1 in the TNBC patient cohort and primary cells by in situ hybridization(ISH),northern blot,fluorescent in situ hybridization(FISH)and cell nucleus/cytoplasm RNA fraction isolation.High AFAP1-AS1 expression was negatively correlated with overall survival(OS),disease-free survival(DFS),metastasis-free survival(MFS)and recurrence-free survival(RFS)in TNBC patients.We explored the function of AFAP1-AS1 by transwell,apoptosis,immunofluorescence(IF)and patient-derived xenograft(PDX)models in vitro and in vivo.We found that AFAP1-AS1 promoted TNBC primary cell survival by inhibiting mitotic catastrophe and increased TNBC primary cell growth,migration and invasion.Mechanistically,AFAP1-AS1 activated phosphorylation of the mitosis-associated kinase PLK1 protein.Elevated levels of AFAP1-AS1 in TNBC primary cells increased PLK1 pathway downstream gene expression,such as CDC25C,CDK1,BUB1 and TTK.More importantly,AFAP1-AS1 increased lung metastases in a mouse metastasis model.Taken together,AFAP1-AS1 functions as an oncogene that activates the PLK1 signaling pathway.AFAP1-AS1 could be used as a potential prognostic marker and therapeutic target for TNBC.

Mitotic Catastrophe的研究进展

细胞死亡是多细胞生物生命过程中重要的生理或病理现象,可分为坏死和程序性细胞死亡,而后者根据死亡细胞的形态学和发生机制的不同又可分为凋亡、自吞噬和mitotic catastrophe,其中mitotic catastrophe是近年来才被揭示报道,是指细胞在有丝分裂过程中死亡的现象,是一种发生在细胞有丝分裂期由于异常的细胞分裂而导致的细胞死亡,它常常伴随着细胞有丝分裂检查点的异常和基因或纺锤体结构的损伤而发生。现对mitotic catastrophe及相关的调控机制进行综述。

Application of Catastrophe Theory in 3D Seismic Data Interpretation of Coal Mine

In order to detect fault exactly and quickly, cusp catastrophe theory is used to interpret 3D coal seismic data in this paper. By establishing a cusp model, seismic signal is transformed into standard form of cusp catastrophe and catastrophe parameters, including time-domain catastrophe potential, time-domain catastrophe time, frequency-domain catastrophe potential and frequency- domain degree, are calculated. Catastrophe theory is used in 3D seismic structural interpretation in coal mine. The results show that the position of abnormality of the catastrophe parameter profile or curve is related to the location of fault, and the cusp catastrophe theory is effective to automatically pick up geology information and improve the interpretation precision in 3D seismic data.

Evaluation of the propensity for coal spontaneous combustion based on catastrophe theory

Generally, different prevention measures should be taken according to spontaneous combustion propensities. The current methods to evaluate the propensity of coal spontaneous combustion, such as chromatographic method of oxygen adsorption, oxidation kinetics method and activation energy method, are mostly affected by human factors. Their boundaries among different classes of propensities were all established by subjective judgments. A new evaluation method using catastrophe theory is introduced. This method can accurately depict the process of coal spontaneous combustion and the evaluation index, ＂catastrophe temperature＂, be obtained based on the model. In terms of catastrophe temperature, the spontaneous combustion propensity of different coals can be sequenced. Experimental data indicate that this method is appropriate to describe the spontaneous combustion process and to evaluate the propensity of coal svontaneous combustion.

Risk Measure and Premium Distribution on Catastrophe Reinsurance

In this paper, we propose a new risk measure which is based on the Or- licz premium principle to characterize catastrophe risk premium. The intention is to develop a formulation strategy for Catastrophe Fund. The logarithm equivalent form of reinsurance premium is regarded as the retention of reinsurer, and the differential earnings between the reinsurance premium and the reinsurer＇s retention is accumu- lated as a part of Catastrophe Fund. We demonstrate that the aforementioned risk measure has some good properties, which are further confirmed by numerical simu- lations in R environment.

Establishment and Application of Assessment Indicator System of Agricultural Catastrophe Vulnerability

To give play to the role of agricultural catastrophe risk fund in spreading agricultural catastrophe risk,we select natural conditions,economic conditions,social conditions,as the external vulnerability assessment indicators;select commodity rate of agricultural products,substitutability of agricultural products,the extent of agricultural products being related to the national economy and the people's livelihood,as the internal vulnerability assessment indicators.We assign weight to indicators using Analytic Hierarchy Process,and establish assessment indicator system of agricultural catastrophe vulnerability,to analyze the compensation for losses of different agricultural products arising from agricultural catastrophe in different regions.And we take the case of rice in Sichuan Province,to demonstrate the role this indicator system.

Safety thickness analysis of tunnel floor in karst region based on catastrophe theory

Based on the tunnel shape, span and depth, the previous elliptical plate model and clamped beam model were modified.The modified model was applied to different situations. For the elliptical plate model, the water effects were considered. For the clamped beam model, water and horizontal stress were considered. Corresponding potential functions and cusp catastrophe models of rock system were established based on the catastrophe theory. The expressions of critical safety thickness were derived with necessary and sufficient conditions. The method was applied to the practical engineering. Some parameters related to the stability were discussed. The results show that elastic modulus and thickness are advantageous to the floor stability, and that the load, span,horizontal stress and water are disadvantageous to the floor stability.

Catastrophe theory-based risk evaluation model for water and mud inrush and its application in karst tunnels

This paper presents a risk evaluation model of water and mud inrush for tunnel excavation in karst areas.The factors affecting the probabilities of water and mud inrush in karst tunnels are investigated to define the dangerousness of this geological disaster.The losses that are caused by water and mud inrush are taken into consideration to account for its harmfulness.Then a risk evaluation model based on the dangerousness-harmfulness evaluation indicator system is constructed,which is more convincing in comparison with the traditional methods.The catastrophe theory is used to evaluate the risk level of water and mud inrush and it has great advantage in handling problems involving discontinuous catastrophe processes.To validate the proposed approach,the Qiyueshan tunnel of Yichang-Wanzhou Railway is taken as an example in which four target segments are evaluated using the risk evaluation model.Finally,the evaluation results are compared with the excavation data,which shows that the risk levels predicted by the proposed approach are in good agreements with that observed in engineering.In conclusion,the catastrophe theory-based risk evaluation model is an efficient and effective approach for water and mud inrush in karst tunnels.

Application of cusp catastrophe theory to reliability analysis of slopes in open-pit mines

A method of slope reliability analysis was developed by imposing a state equation on the limit equilibrium theory, given the basis of a fixed safety factor technique. Among the many problems of reliability analysis, the most important problem is to find a performance function. We have created a new method of building a limit state equation for planar slip surfaces by applying the mathematical cusp catastrophe theory. This new technique overcomes the defects in the traditional rigid limit equilibrium theory and offers a new way for studying the reliability problem of planar slip surfaces. Consequently, we applied the technique to a case of an open-pit mine and compared our results with that of the traditional approach. From the results we conclude that both methods are essentially consistent, but the reliability index calculated by the traditional model is lower than that from the catastrophic model. The catastrophe model takes into consideration two possible situations of a slope being in the limit equilibrium condition, i.e., it may or may not slip. In the traditional method, however, a slope is definitely considered as slipping when it meets the condition of a limit equilibrium. We conclude that the catastrophe model has more actual and instructive importance compared to the traditional model.

Application of the catastrophe progression method in predicting coal and gas outburst

Based on catastrophe theory,we used the catastrophe progression method to predict the risk of coal and gas outbursts in coal mines.According to the major factors affecting coal and gas outbursts,we built a comprehensive evaluation index system and a coal and gas outburst prediction model.In addition,we performed a standard transformation for each index system;based on the degree the various indices affect the risk of an outburst,to make the data dimensionless.Based on the outburst data from eight mines,we determined catastrophe progression values and verified these values.The results show that:1) converting multi-dimensional problems into one-dimensional problems using this catastrophe progression method can simplify the steps of predicting coal and gas outbursts;2) when pre-determined catastrophe progression values are used to predict coal and gas outbursts,the predicting accuracy rate can be as high as 87.5%;3) the various coal mines have different factors inducing outbursts with varying importance of these factors and 4) the catastrophe progression values,calculated based on these factors,can be used effectively to predict the risk of outbursts in coal mines.

Assessment of Flood Catastrophe Risk for Grain Production at the Provincial Scale in China Based on the BMM Method

Flood catastrophe risk assessment is imperative for the steady development of agriculture under the context of global climate change,and meanwhile,it is an urgent scientific issue need to be solved in agricultural risk assessment discipline.This paper developed the methodology of flood catastrophe risk assessment,which can be shown as the standard process of crop loss calculation,Monte Carlo simulation,the generalized extreme value distribution（GEV） fitting,and risk evaluation.Data on crop loss were collected based on hectares covered by natural disasters,hectares affected by natural disasters,and hectares destroyed by natural disasters using the standard equation.Monte Carlo simulation based on appropriate distribution was used to expand sample size to overcome the insufficiency of crop loss data.Block maxima model（BMM） approach based on the extreme value theory was for modeling the generalized extreme value distribution（GEV） of flood catastrophe loss,and then flood catastrophe risk at the provincial scale in China was calculated.The Type III Extreme distribution（Weibull） has a weighted advantage of modeling flood catastrophe risk for grain production.The impact of flood catastrophe to grain production in China was significantly serious,and high or very high risk of flood catastrophe mainly concentrates on the central and eastern regions of China.Given the scenario of suffering once-in-a-century flood disaster,for majority of the major-producing provinces,the probability of 10% reduction of grain output is more than 90%.Especially,the probabilities of more than 15% decline in grain production reach up to 99.99,99.86,99.69,and 91.60% respectively in Anhui,Jilin,Liaoning,and Heilongjiang.Flood catastrophe assessment can provide multifaceted information about flood catastrophe risk that can help to guide management of flood catastrophe.

CUSP CATASTROPHE MODEL OF INSTABILITY OF PILLAR IN ASYMMETRIC MINING

A simplified mechanical model of pillar-hang wall was established in asymmetric mining and instability of the system was discussed by means of potential energy principle and cusp catastrophe theory. The necessary-sufficient condition and the jump value of displacement of pillar and the released energy expressions were derived, which established foundation for quantifying of the instability of system. The results show that instability of the system is related to load and its stiffness distribution. The critical load increases with the increasing relative stiffness, and the system is more stable. On the contrary, the instability of system is likely to occur, and the released energy is larger in instability process, and the harm is more tremendous accordingly. Furthermore, an example was calculated, and the estimated results are in good agreement with the practical experience, which provide basis for mining order and arranging stope.

DESCRIPTION AND PREDICTION OF CATASTROPHE OF VIBRATION STATE FOR FAULTY ROTORS

A sudden increase of vibration amplitude with no foreboding often results in an abrupt breakdown of a mechanical system.The catastrophe of vibration state of a faulty rotor is a typical nonlinear phenomenon,and very difficult to be described and predicted with linear vibration theory.On the basis of nonlinear vibration and catastrophe theory,fhe eatastrophe of the vibration amplitude of the faulty rotor is described;a way to predict its emergence is developed.

Fold catastrophe model of dynamic pillar failure in asymmetric mining

A rock burst disaster not only destroys the pit facilities and results in economic loss but it also threatens the life of the miners. Pillar rock burst has a higher frequency of occurrence in the pit compared to other kinds of rock burst. Understanding the cause, magnitude and prevention of pillar rock burst is a significant undertaking. Equations describing the bending moment and displacement of the rock beam in asymmetric mining have been deduced for simplified asymmetric beam-pillar systems. Using the symbolic operation software MAPLE 9.5 a catastrophe model of the dynamic failure of an asymmetric rock-beam pillar system has been established. The differential form of the total potential function deduced from the law of conservation of energy was used for this deduction. The critical conditions and the initial and final positions of the pillar during failure have been given in analytical form. The amount of elastic energy released by the rock beam at the instant of failure is determined as well as. A diagrammatic form showing the pillar failure was plotted using MATLAB software. This plot contains a wealth of information and is important for understanding the behavior during each deformation phase of the rock-beam pillar system. The graphic also aids in distinguishing the equivalent stiffness of the rock beam in different directions.

Bifurcation and catastrophe of seepage flow system in broken rock

The study of dynamical behavior of water or gas flows in broken rock is a basic research topic among a series of key projects about stability control of the surrounding rocks in mines and the prevention of some disasters such as water inrush or gas outburst and the protection of the groundwater resource. It is of great theoretical and engineering importance in respect of promo- tion of security in mine production and sustainable development of the coal industry. According to the non-Darcy property of seepage flow in broken rock dynamic equations of non-Darcy and non-steady flows in broken rock are established. By dimensionless transformation, the solution diagram of steady-states satisfying the given boundary conditions is obtained. By numerical analysis of low relaxation iteration, the dynamic responses corresponding to the different flow parameters have been obtained. The stability analysis of the steady-states indicate that a saddle-node bifurcaton exists in the seepage flow system of broken rock. Consequently, using catastrophe theory, the fold catastrophe model of seepage flow instability has been obtained. As a result, the bifurcation curves of the seepage flow systems with different control parameters are presented and the standard potential function is also given with respect to the generalized state variable for the fold catastrophe of a dynamic system of seepage flow in broken rock.

Catastrophe stability analysis for shallow tunnels considering settlement

Limit analysis of the stability of geomechanical projects is one of the most difficult problems.This work investigates the influences of different parameters in NL failure strength on possible collapsing block shapes of single and twin shallow tunnels with considering the effects of surface settlement.Upper bound solutions derived by functional catastrophe theory are used for describing the distinct characteristics of falling blocks of different parts in twin tunnels.Furthermore the analytical solutions of minimum supporting pressures in shallow tunnels are obtained by the help of the variational principle.Lastly,the comparisons are made both in collapsed mechanism and stability factor with different methods.According to the numerical results in this work,the influences of different parameters on the size of collapsing block are presented in the tables and the limit supporting loads are illustrated in the form graphs that account for the surface settlement.

Catastrophe analysis of deep tunnel above water-filled caves

To explore the influence of karst cavity pressure on the failure mechanisms of rock layers above water-filled caves, novel blow-out and collapse mechanisms are put forward in this study. The proposed method uses the nonlinear optimization to obtain the failure profiles of surrounding layered rock with water-filled cave at the bottom of the tunnel. By referring to the functional catastrophe theory, stability analysis with different properties in different rock layers is implemented with considering the incorporation of seepage forces since the groundwater cannot be ignored in the catastrophe analysis of deep tunnel bottom. Also the parametric analysis is implemented to discuss the influences of different rock strength factors on the failure profiles. In order to offer a good guide of design for the excavation of deep tunnels above the water-filled caves, the proposed method is applied to design of the minimum effective height for rock layer. The results obtained by this work agree well with the existing published ones.

Catastrophe analysis on pillar instability considered mining effect

The instability of the pillar was discussed based on the potential energy principle and the cusp catastrophe theory, and a simplified mechanical model of the pillar was established considering the mining effect. The necessary-sufficient conditions, the jump value of displacement of pillar and the released energy expressions were deduced. The results show that the instability of the pillar is related to the properties of the rock, the external force and the relative stiffness of the elastic area to the plastic area. The instability of system is like to occur with the enlarging of the softening area or the decreasing of E/λ. The calculation done shows that the estimated results correspond to practical experience.