Research On Meteorological Disaster Risk Assessment Method Based On Ruin Theory

Meteorological disasters are concomitant with the healthy development of society,and it caused huge economic losses to people all over the world.Due to the impact of global warming,the future global extreme weather disasters may be prone to multiple,frequent and recurring trends,which poses great risks to global agricultural production safety.At the same time,with the increase of the exposure of economic development,the economic losses caused by future meteorological disasters will increase.However,China has a large population base,with low per capita arable land and water shortage.At the same time,China has a series of problems,such as serious water pollution,serious desertification and soil erosion,severe grassland ecology,severe marine ecology and deteriorating atmospheric environment.Therefore,it has become an important scientific basis for the sustainable development of economy to explore the mechanism of disaster risk formation and assess the risk of disaster.At present,the research on disaster risk has a certain basis,but this kind of research mainly carries out risk assessment from the perspective of risk factors such as hazards,vulnerability and exposure.In addition,these researches mainly examine meteorological risks from the perspective of risk aversion,and ignore the difference of risk tolerance,i.e.the group differences that cannot distinguish risk aversion and risk pursuit.The word "risk" comes from economics,but the assessment of meteorological disasters from the perspective of mathematical economy is very rare.The studies of risk in the economy have been developing for hundreds of years,therefore,this paper attempts to carry out the research on the risk assessment methods of meteorological disasters from the perspective of mathematical economics.In this paper,we first use the utility definition in economics to transform the focus of the previous evaluation from the assessment of loss size into the evaluation of utility size,so as to make the model reflect the characteristics of the risk bearing body,which is also much closer to the risk perception of the body.On the basis of summarizing the definition of risk,afresh from the Angle of utility,the paper puts forward the definition of risk,namely the future risk within a certain period of time the body for the future potential losses show the degree of concern.Then,the utility change is regarded as the fluctuation process of a linear growth trend,and the fluctuation is the change of meteorological factors.The random mathematical equation can be used to describe the fluctuation process.Based on the knowledge of bankruptcy theory,the mathematical expression of the risk in this paper is given,namely,the probability of the utility being lower than the threshold value of the given utility in the stochastic process is solved.In this way,we first discuss the risk model of hazards,vulnerability and exposure,and deduce the expression of risk probability in the process of compound Poisson process.In addition,in the meteorological disaster risk assessment,disaster prevention ability is an important factor in risk assessment,so this article use dependent risk model to discuss the solution under the hypothesis of the compound Poisson process risk probability form.But considering the reality of the stochastic process is not necessarily a good hypothesis conforms to compound Poisson process,and the utility cost size is also difficult to meet the requirements of exponential distribution,so based on the compound Poisson process risk probability form solutions are difficult to directly used in the analysis of the actual problem.For this purpose,this paper discusses the probability distribution function given by the maximum entropy principle to transform the general process into the possibility of satisfying the compound Poisson process,and the computer simulation method is used to verify it.Finally,the paper takes drought as an example to compare the conventional copula method and the risk analysis method presented in this paper.The main results of this paper are:(1)The long-term risk process can be described by stochastic equation.And according to the difference between initial utility and utility threshold,the risk process can be divided into two types:one is the positive risk process and the other is the negative risk process.We have obtained the general expression of the risk probability under the assumption of the compound Poisson process,and given the special solution form when the utility loss satisfies the exponential distribution.(2)The general expression and Lundberg inequality of the risk probability of the two kinds of risk processes under the assumption of the compound Poisson process are obtained by considering the disaster prevention and reduction items as the dependent process of the utility loss.(3)Distribution function based on maximum entropy principle can be a very good fitting drought duration and drought intensity distribution,and based on the distribution of two-dimensional probability analysis model is superior to the conventional use of exponential distribution and the Gamma distribution fitting respectively drought duration and intensity of drought.(4)Computer simulation shows that the distribution function given by the maximum entropy principle can convert the waiting interval to the sample that is in accordance with the exponential distribution.This makes the general process become possible to satisfy the compound Poisson process,and the risk probability obtained by computer simulation is well consistent with the theoretical calculation.(5)Using the SPI data of the monthly scale and the analysis of the Copula method,it shows that China's drought center has obvious cycle characteristics.From 1961 to 2015,every 10 years,the position of the drought center is located in north China-northeast-southwest ?north-northeast-southwest.Based on the same SPI data,the intensity of drought waiting interval and drought intensity was obtained,and the intensity is considered as the utility loss due to each drought.The results show that the interval of the drought waiting interval satisfies the exponential distribution and the utility loss can be also expressed by the exponential distribution.Based on the risk probability of the compound Poisson process,the overall risk of 1961-2015 and the risk of every 10 years were calculated.The results show that the overall risk characteristics of 1961-2015 in the south of China,especially in the south of the Yangtze river,and the risk of the northeast region and the northern region of Sinkiang are higher than that of other regions.The calculation of risk probability per 10 years indicates that the spatial distribution of risk and the results obtained by using the Copula method have a high spatial consistency.