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.

List of 85 typical catastrophic landslides from March 2004 to February 2024

Landslides are one of the most dangerous natural hazards that cause significant property damage and loss of life.Landslides often destroy farmland,villages,houses,factories,schools,roads and other facilities,injuring humans and livestock.Sometimes,entire towns are devastated by landslides.Due to their pervasiveness,varied triggering factors,and sudden occurrence,landslides are currently one of the most challenging natural disasters to prevent and mitigate.

Subarachnoid hemorrhage misdiagnosed as acute coronary syndrome leading to catastrophic neurologic injury: A case report

BACKGROUND Elevated levels of cardiac troponin and abnormal electrocardiogram changes are the primary basis for clinical diagnosis of acute coronary syndrome(ACS).Troponin levels in ACS patients can often be more than 50 times the upper reference limit.Some patients with subarachnoid hemorrhage(SAH)also show electrocardiogram abnormalities,myocardial damage,and elevated cardiac biomarkers.Unlike ACS patients,patients with SAH only have a slight increase in troponin,and the use of anticoagulants or antiplatelet drugs is prohibited.Because of the opposite treatment modalities,it is essential for clinicians to distinguish between SAH and ACS.CASE SUMMARY A 56-year-old female patient was admitted to the emergency department at night with a sudden onset of severe back pain.The final diagnosis was intraspinal hematoma in the thoracic spine.We performed an emergency thoracic spinal canal hematoma evacuation procedure with the assistance of a microscope.Intraoperatively,diffuse hematoma formation was found in the T7-T10 spinal canal,and no obvious spinal vascular malformation changes were observed.Postoperative head and spinal magnetic resonance imaging(MRI)showed a small amount of SAH in the skull,no obvious abnormalities in the cervical and thoracic spinal canals,and no abnormal signals in the lumbar spinal canal.Thoracoab-dominal aorta computed tomography angiography showed no vascular malfor-mation.Postoperative motor system examination showed Medical Research Council Scale grade 1/5 strength in both lower extremities,and the patient experienced decreased sensation below the T12 rib margin and reported a Visual Analog Scale score of 3.CONCLUSION Extremely elevated troponin levels(more than 50 times the normal range)are not unique to coronary artery disease.SAH can also result in extremely high troponin levels,and antiplatelet drugs are contraindicated in such cases.Emergency MRI can help in the early differential diagnosis,as a misdiagnosis of ACS can lead to catastrophic neurological damage in patients with spontaneous spinal SAH.

Research progress of pain catastrophizing in patients with lumbar disc herniation

Pain catastrophization is one of the negative emotional factors and an important psychological factor associated with patients with lumbar disc herniation(LDH).Currently,the concept of pain catastrophization of LDH is relatively mature abroad;however,there are only few research studies on this in China.To understand the status quo of pain catastrophization(PC)in patients with LDH and its influencing factors,the intervention measures of PC and their efficacy were further analyzed.In the present paper,the research status of PC at home and abroad is briefly expounded,and the influencing factors and clinical intervention measures for PC are analyzed.This paper reviews the concept of PC,the assessment tools,influencing factors,and the relevant intervention measures.In order to evaluate the pain degree of patients,understand the incidence of pain in patients,and improve the cure rate and quality of life of patients,the basic situation of patients with pain disaster is summarized to provide reference for medical personnel.

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。

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.

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.

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.

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.

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.

PRICING CATASTROPHE OPTIONS WITH COUNTERPARTY CREDIT RISK IN A REDUCED FORM MODEL

In this paper, we study the price of catastrophe Options with counterparty credit risk in a reduced form model. We assume that the loss process is generated by a doubly stochastic Poisson process, the share price process is modeled through a jump-diffusion process which is correlated to the loss process, the interest rate process and the default intensity process are modeled through the Vasicek model： We derive the closed form formulae for pricing catastrophe options in a reduced form model. Furthermore, we make some numerical analysis on the explicit formulae.

A CATASTROPHE ANALYSIS ON THE STABILITY OF THE CRACK GROWTH IN THREE-POINT BENDING SPECIMENS

This paper presents an attempt at the application of catastrophe theory to the stability analysis of J-controlled crack growth in three-point bending specimens. By introducing the solutions of J-integral in the completely yielding state for the ideal plastic material, the critical condition of losing stability for the crack propagation in the specimen is obtained, based on the cusp catastrophe theory. The process of the crack growth from geometrical sense is described.

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.

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.

GEOGRAPHIC ENVIRONMENT CHANGE AND FLOOD CATASTROPHE IN HUAIHE RIVER BASIN DURING LAST 2000 YEARS

During the last 2000 years,flood and waterlogging catastrophes took place quite frequently in the Huaihe River Basin.In the authors’opinion,these natural calamities have a very close relation to the evolution of Hongze Lake.Formed initially within a man-made dyke that was built in the Han Dynasty about 2000 years ago, Hongze Lake brought out headward accumulation developing in the middle reaches of the Huaihe River, with its continuous aggravation on lake-bottom and consequent water-level rise. It was estimated that,on an average,there were 3400×104t sediment per kilometre per year deposited on the river bed from Lutaizi to Bengbu.Therefore,the rising of water-level and the drainage difficulty in the middle reaches of the Huaihe River aggravated local flood and waterlogging catastrophe here.

Roll stability catastrophe mechanism of a flooded ship on regular sea waves

Based on a typical one-free-degree ship roll motion equation, the cusp catastrophe model is built including the bifurca- tion set equation, splitting factor ＇u＇ and regular factor ＇v＇, where both ＇u＇ and ＇v＇ are further expressed with typical flooded ship parameters. Then, the roll catastrophe mechanism is analyzed mainly by means of ＇u＇, under the given parameters of a typical trawler boat. The aim of this research is to reveal the mutagenic mechanism of the roll stability and provide a reference for improving ship roll stability.

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.