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.

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.

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.

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.

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.

A CATASTROPHIC MODEL FOR VIBRATIONAL BUCKLING OF ELASTIC ARCHES

This paper represents an attempt at the application of catastrophe theory to the dynamic stability of engineering structures. The authors not only obtain a catastrophic model of vibrational buckling of elastic arches, but also give the critical condition of losing stability.

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.

Recent catastrophic landslides and mitigation in China

Increasing population density and development of mountainous terrain have brought human settlements within reach of landslide hazards.In recent years,due to the shortening of return period for severe natural events such as heavy rainfall,snowline retreating,great earthquake together with human activities,catastrophic landslides happened more frequently than before,resulting in large-scale casualties due to the increasing occurrences of rapid long-runout rock avalanches,especially in China.This paper presents some typical case histories related to the catastrophic landslides,including the Guanling rock avalanche,the Yigong rockslide-debris avalanche,the Wenchuan earthquake-induced landslides and the Danba landslide.They occurred in the last decade.Moreover,taking the Jiweishan catastrophic rockslide-fragment flow and the Yuhuangge landslide located in the new Wushan Town for examples,early-warning system and risk management on landslides are discussed in detail.

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.

Stress analysis on large-diameter buried gas pipelines under catastrophic landslides

This paper presents a method for analysis of stress and strain of gas pipelines under the effect of horizontal catastrophic landslides. A soil spring model was used to analyze the nonlinear characteristics concerning the mutual effects between the pipeline and the soil. The Ramberg–Osgood model was used to describe the constitutive relations of pipeline materials. This paper also constructed a finite element analysis model using ABAQUS finite element software and studied the distribution of the maximum stress and strain of the pipeline and the axial stress and strain along the pipeline by referencing some typical accident cases. The calculation results indicated that the maximum stress and strain increased gradually with the displacement of landslide.The limit values of pipeline axial stress strain appeared at the junction of the landslide area and non-landslide area. The stress failure criterion was relatively more conservative than the strain failure criterion. The research results of this paper may be used as a technical reference concerning the design and safety management of large-diameter gas pipelines under the effects of catastrophic landslides.

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.

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.

Catastrophic mechanism of coal and gas outbursts and their prevention and control

Based on the engineering observations of coal and gas outbursts during mining processes and the experimental results,we built a thin plate mechanical model for layered and spalled coal bodies.We studied the mechanical mechanism of outbursts,due to instability,of thin plates of coal rocks under the action of in-plane load and normal load,by using the catastrophe theory.The total potential function is derived for the layered rock system,the cusp catastrophe model for the system is established,the bifurcation set that makes the system unstable is given,the process in which gradual change of action forces leads to catastrophic change of state is analyzed,and the effect of movement path of point(P,q) in the control space on the stability of rock plate is analyzed.The study results show that during the process of coal mining,the stability of the layered coal bodies depends not only on its physical properties and dimensions but also on the magnitudes and changing paths of the in-plane load and the normal load.When the gas in the coal bodies ahead of the mining face is pre-drained,the gas pressure can be reduced and the normal load q can be lowered.Consequently,disasters such as coal and gas outbursts can be effectively prevented.