阅读说明：本技术 巨灾事件模型的平均损失的查表校正方法 (Table lookup correction method for average loss of catastrophe event model ) 是由 杨浩 袁曦 鲁涵 刘邈 于 2021-08-06 设计创作，主要内容包括：本发明涉及一种巨灾事件模型的平均损失的查表校正方法,包括读参步骤、建表步骤、计算步骤和校正步骤；和一种计算机程序产品,计算机程序/指令被处理器执行时实现本发明的技术方案；还有一种计算系统,其中至少有一个处理器,以及存储器,其存储有指令,当通过至少一个处理器来执行该指令时,实现本发明的技术方案。本发明具体地提出了依据巨灾事件模型的ELT生成超越概率分布表的技术方案,通过借助该超越概率分布表对事件的平均损失进行调整或校正,从而实现事件的损失能够考虑二次不确定性。(The invention relates to a table look-up correction method for average loss of a disaster event model, which comprises a parameter reading step, a table building step, a calculation step and a correction step; and a computer program product, the computer program/instructions implementing the solution of the invention when executed by a processor; there is also a computing system having at least one processor and a memory storing instructions that, when executed by the at least one processor, implement aspects of the present invention. The invention specifically provides a technical scheme for generating the transcendental probability distribution table according to the ELT of the catastrophe event model, and the average loss of the event is adjusted or corrected by the transcendental probability distribution table, so that the loss of the event can consider secondary uncertainty.)

1. A table look-up correction method for average loss of a catastrophic event model is characterized by comprising the following steps:

reading ELT data of the catastrophic event model in the parameter reading step, wherein the ELT comprises average loss;

establishing a transcendental probability distribution table according to the ELT, wherein the transcendental probability distribution table comprises a plurality of loss values and transcendental probability OEP corresponding to each loss value;

calculating the transcendental probability according to the ELT;

and a correction step of comparing each calculated transcendental probability with the transcendental probabilities in the distribution table, correcting the loss value of the calculated transcendental probability by a linear interpolation method, and replacing the average loss with the obtained correction loss.

2. The method of claim 1, wherein the OEP for each loss value is calculated using as parameters the frequency of occurrence of catastrophic events and the CEP for the loss value for the event of only one catastrophic event.

3. The method of claim 2, wherein said step of building a table specifically comprises the steps of:

sampling in the value range of the loss value L, and calculating the OEP (L is more than or equal to L) of each sampling point L according to the formula I:

OEP(L≥l)＝1-e^{-λ×CEP(L≥l)}formula I

Wherein, L is a loss value, L is a sampling point, OEP is an override probability, and OEP (L is more than or equal to L) is the probability that the loss value L is more than or equal to the sampling point L; CEP is the exceeding probability under the condition that only one catastrophic event occurs, CEP (L is more than or equal to L) is the probability that the loss value L is more than or equal to the sampling point L under the condition that only one catastrophic event occurs; e is a natural base number; λ is the total frequency of occurrence of the simulated catastrophic event;

recording the over-ride probability OEP of each sampling point in the value range of the L and storing the over-ride probability OEP as a table.

4. The method according to claim 3, wherein the probability of exceeding CEP (L ≧ L) under the condition of only one catastrophic event for each of the sample points L with a loss value L greater than or equal to is calculated according to formula II:

wherein, L is a loss value, L is a sampling point, CEP (L is more than or equal to L) is the probability that the loss value L is more than or equal to the sampling point L under the condition that only one catastrophic event occurs; i is an integer with the value from 1 to n, wherein n is the number of the simulated catastrophic events; EventFre_iThe occurrence frequency of the ith simulated catastrophic event; ps_i(L is more than or equal to L) is the survival function of the ith simulated disaster event, wherein the loss value of the ith simulated disaster event is more than or equal to the sampling point L.

5. The method of claim 4, wherein each of said Ps is calculated according to formula III_i(L≥l)：

Wherein L is a loss value; i is an integer with the value from 1 to n, wherein n is the number of the simulated catastrophic events; ps_i(L ≧ L) is the ith simulated macroThe loss value of the disaster event is greater than or equal to the survival function of the sampling point l; f. of_i(x) And the probability density function of the ith simulated catastrophic event loss value being greater than or equal to the sampling point l is adopted.

6. The method of claim 5, wherein the probability of each of the simulated catastrophic events is subject to one of a beta distribution, a normal distribution, a binomial distribution, or a logarithmically binomial distribution.

7. The method of claim 5, wherein each of said f is calculated according to formula IV_i(x)：

Wherein i is an integer with a value from 1 to n, and n is the number of the simulated catastrophic events; f. of_i(x) The probability density function of the ith simulated catastrophic event loss value being greater than or equal to the sampling point l; α is a first parameter of the probability distribution obeyed by the ith simulated catastrophic event, and β is a second parameter of the probability distribution obeyed by the ith simulated catastrophic event.

8. The method of claim 7, wherein α and β are calculated according to formula V and formula VI, respectively:

wherein i is an integer with a value from 1 to n, and n is the number of the simulated catastrophic events; alpha is the first parameter of probability distribution obeyed by the ith simulated flood event, and beta isA probability distribution second parameter obeying to the ith simulated disaster event; loss_iIs the average loss value, Exp, of the ith simulated catastrophic event_iThe loss maximum value of the ith simulated catastrophic event; STDV_iIs the loss standard deviation of the ith simulated catastrophic event.

9. A computer program product comprising computer programs/instructions, characterized in that the computer programs/instructions, when executed by a processor, implement the steps of the method according to claims 1-8.

10. A computing system, characterized in that the system comprises at least one processor; and a memory storing instructions which, when executed by the at least one processor, perform the steps of the method according to any one of claims 1 to 8.

Technical Field

The invention relates to the field of reinsurance, in particular to a table look-up correction method for average loss of a catastrophic event model.

Background

In the process of calculating loss of the catastrophic event and pricing, the system firstly needs to perform event simulation according to the catastrophic event model, that is, to generate the actual occurrence condition of the catastrophic event. When the system carries out disaster event simulation, the actual occurrence condition YLT (Year Loss Table) of the event is generated according to event information ELT (event Loss Table) in the disaster model, and according to the YLT, the system calculates an over-probability curve OEP (occupancy Exception Proavailability), wherein OEP represents the probability OEP (X) that the Loss of the event with the largest Loss exceeds a certain value X in the events which occur every year.

In the process of making the transcendental probability curve, only the average value of loss is considered, and the uncertainty of loss even if an event occurs is not considered, namely, only the primary uncertainty (namely parameter risk) is considered, and the secondary uncertainty (namely process risk) is not considered. This is not a big problem in the cumulative analysis of disaster risks by the insured company, however, secondary uncertainty may have some impact on valuation in the reinsurance company's view if it is doing an overdesign business. This is mainly because if the average loss of an event is 990 ten thousand yuan and the point of claim initiation of a super claim is 1000 ten thousand yuan, the loss cost of the super claim is zero regardless of the risk of the process. However, due to the risk of the process, the loss event has a certain probability of causing the loss to the overdue.

Disclosure of Invention

In order to solve the above technical problems, a technical solution of the present invention provides a lookup table correction method for average loss of a catastrophic event model, which corrects average loss in an original catastrophic event model by establishing an transcendental probability distribution table considering secondary uncertainty, comprising the following steps:

reading ELT data of the catastrophic event model in the parameter reading step, wherein the ELT comprises average loss;

establishing a transcendental probability distribution table according to the ELT, wherein the transcendental probability distribution table comprises a plurality of loss values and transcendental probability OEP corresponding to each loss value;

calculating the transcendental probability according to the ELT;

and a correction step of comparing each calculated transcendental probability with the transcendental probabilities in the distribution table, correcting the loss value of the calculated transcendental probability by a linear interpolation method, and replacing the average loss with the obtained correction loss.

The invention also proposes a computer program product comprising a computer program/instructions which, when executed by a processor, implement the solution of the invention.

The invention also provides a computing system, characterized in that the system comprises at least one processor; and a memory storing instructions that, when executed by the at least one processor, implement aspects of the present invention.

The invention has the advantages that the technical scheme of generating the transcendental probability distribution table according to the ELT of the catastrophe event model is specifically provided, and the average loss of the event is adjusted or corrected by the transcendental probability distribution table, so that the loss of the event can consider secondary uncertainty.

Drawings

Fig. 1 is a flowchart of a method for correcting average loss in a look-up table type catastrophic event model.

Detailed Description

The technical solution of the present invention is specifically explained below with reference to the accompanying drawings. In various embodiments, the method of the present invention may be used as a preprocessing method for a disaster event loss risk model, as shown in fig. 1, and includes the following steps:

reading ELT data of the catastrophic event model in the parameter reading step, wherein the ELT comprises average loss;

the table building step is that a transcendental probability distribution table is built according to the ELT, and the transcendental probability distribution table comprises a plurality of loss values and transcendental probability OEP corresponding to each loss value;

calculating the transcendental probability according to the ELT;

and the correction step compares each calculated transcendental probability with the transcendental probabilities in the distribution table, corrects the loss value of the calculated transcendental probability by a linear interpolation method, and replaces the average loss with the obtained correction loss.

Generally, each piece of information of the "ELT of the disaster event model" (as shown in table 1) includes information of one event, and each piece of information includes the following 5 fields:

1. EventId: the identification of the event is carried out,

2. eventfrequency: the frequency of the annual occurrence of the event,

3. EventLoss: the mean value of the loss of the event,

4. EventSTDV: the loss of the standard deviation of the event,

5. EventExposure: loss maximum for an event;

TABLE 1 ELT of catastrophe event model

EventId	EventFrequency	EventLoss	EventSTDV	EventExposure
					10000	0.2	1500000	800000	5500000
20000	0.3	3000000	2000000	15000000
					30000	0.4	6500000	5000000	50000000

The term "transcendental probability distribution table" is shown in table 2, wherein the Loss column indicates the Loss value of the event with the highest Loss occurring every year, and the OEP column indicates the probability that the Loss value of the event with the highest Loss occurring in one year is equal to or greater than the Loss value.

TABLE 2 transcendental probability distribution Table

Loss	OEP
		7000000	0.1
6600000	0.2
		6400000	0.3
6000000	0.4
		3400000	0.5
3100000	0.6
		3000000	0.7
2900000	0.8
		1600000	0.9

The transcendental probability distribution table can be stored in a computer as a preset module, and data shown in table 2 can be directly read when the technical scheme of the invention is executed.

In some embodiments, the over-ride probability OEP corresponding to each loss value is parameterized by the frequency of occurrence of catastrophic events and the over-ride probability CEP corresponding to the loss value under the condition that only one catastrophic event occurs.

Wherein, the annual occurrence condition of the disaster event obeys the poisson distribution. The present embodiment includes a program implementation in which the override function OEP is the primary function.

In some embodiments, the step of building a table specifically comprises the steps of:

sampling in the value range of the loss value L, and calculating the OEP (L is more than or equal to L) of each sampling point L according to the formula I:

OEP(L≥l)＝1-e^{-λ×CEP(L≥l)}formula I

Wherein, L is a loss value, L is a sampling point, OEP is an override probability, and OEP (L is more than or equal to L) is the probability that the loss value L of an event is more than or equal to the sampling point L; CEP is the exceeding probability under the condition that only one catastrophic event occurs, CEP (L is more than or equal to L) is the probability that the loss value L is more than or equal to the sampling point L under the condition that only one catastrophic event occurs; e is a natural base number; λ is the total frequency of occurrence of the simulated catastrophic event;

the over-run probability OEP of each sample point within the range of values of L is recorded and stored as a table.

The loss value may range from 0 to infinity, or to a threshold value large enough that no more events than the loss value is expected to occur.

The sampling includes that the value is taken according to a determined step frequency delta in the above value range, and the value is taken as a sampling point.

Cep (conditional expression probability) is the probability that the loss value exceeds a certain value considering the case where only one catastrophic event occurs per year.

In some embodiments, the overrun probability CEP under the condition of occurrence of only one catastrophic event for each of the sampling points L is calculated with a loss value L greater than or equal to (L ≧ L) according to formula II:

wherein, L is a loss value, L is a sampling point, CEP (L is more than or equal to L) is the probability that the loss value L is more than or equal to the sampling point L under the condition that only one catastrophic event occurs; i is an integer with the value from 1 to n, wherein n is the number of the simulated catastrophic events; EventFre_iThe occurrence frequency of the ith simulated catastrophic event; ps_i(L is more than or equal to L) is the survival function of the ith simulated disaster event, wherein the loss value of the ith simulated disaster event is more than or equal to the sampling point L.

In some embodiments, each Ps is calculated according to formula iii_i(L≥l)：

Wherein L is a loss value; i is an integer with the value from 1 to n, wherein n is the number of the simulated catastrophic events; ps_i(L is more than or equal to L) is the survival function of the ith simulated disaster event, wherein the loss value of the ith simulated disaster event is more than or equal to the sampling point L; f. of_i(x) And the probability density function of the ith simulated catastrophic event loss value being greater than or equal to the sampling point l is adopted.

The method for calculating the Integral can adopt the existing methods such as the trap z function and the Integral function of the MATLAB function library.

Some embodiments consider that the probability of each simulated catastrophic event is distributed according to one of a beta distribution, a normal distribution, a binomial distribution, or a log-binomial distribution.

Considering that the occurrence of different catastrophic events may be subject to different probability distribution models, the method of the present invention includes obtaining survival functions for different events from different probability distribution models.

In some embodiments, the probability distributions of the simulated catastrophic events all satisfy the beta distribution, and f in the above embodiments is calculated according to formula iv_i(x)：

Wherein i is an integer with a value from 1 to n, and n is the number of simulated catastrophic events; f. of_i(x) The probability density function of the ith simulated catastrophic event loss value being greater than or equal to the sampling point l; α is a first parameter of a probability distribution obeyed by the ith simulated catastrophic event, and β is a second parameter of the probability distribution obeyed by the ith simulated catastrophic event.

This embodiment considers beta distribution as a distribution model that is more applicable.

Some embodiments, as a more specific step of the above embodiments, the beta distribution parameters α and β are calculated according to formula V and formula VI, respectively:

wherein i is an integer with a value from 1 to n, and n is the number of simulated catastrophic events; alpha is the probability distribution obeyed by the ith simulated catastrophic eventA first parameter, beta is a probability distribution second parameter obeyed by the ith simulated flood event; loss_iIs the average loss value, Exp, of the ith simulated catastrophic event_iThe loss maximum value of the ith simulated catastrophic event; STDV_iIs the loss standard deviation of the ith simulated catastrophic event.

The variables in this embodiment can be obtained from the ELTs read in the parameter reading step.

In some more specific embodiments, wherein the average loss may be calculated as follows:

1. reading ELT data of the disaster event model;

2. the OEP table directly generated by the ELT in the above embodiment is called distributed OEP and is stored in the computer as a preset module (or parameter);

description of the drawings: the distributed OEP curve results have considered the distribution characteristics and uncertainty of the event. After the loss of an event is adjusted by using the distributed OEP curve result, although a certain event appears multiple times in the simulation result, the actual loss of each event is the same and is the adjusted EventLoss value of the event, and the adjusted event does not need to be sampled multiple times, and after the adjustment, the OEP result calculated by the system can be highly matched with the distributed OEP result.

3. Sequencing all events in the ELT in an order from big to small of EventLoss, and assuming that the loss of the ith event after sequencing is EventLoss [ i ], the annual occurrence frequency of the ith event is Eventfrequency [ i ], i is 1,2, … …, and n is the number of the events;

4. for the ith event, firstly calculating the sum of the eventFrequency from the first event to the ith event and eventFrequency Sum [ i ], wherein the eventFrequency Sum [ i ] - [ eventFrequency Sum [ i-1] + Eventfrequency in the actual calculation process;

description of the drawings: for the ith event, the annual average probability of occurrence of all events with losses greater than or equal to the event is the sum of the annual average probability of occurrence of the event with losses greater than the event and the annual average probability of occurrence of the event. The event is sequenced from large to small according to EventLoss, the event with the Loss being more than or equal to the event is the 1 st event to the ith event, the rule is obtained on the premise that distributed OEP has monotonicity, actually the distributed OEP is monotonically decreased, and as EventFrequency Sum [ i ] is certainly larger than Eventfrequencysum [ i-1], the Loss of the event i-1 is still larger than the Loss of the event i after adjustment, and therefore the size relation of the event Loss cannot be changed due to the adjustment.

5. Calculating the probability that the annual maximum loss is greater than or equal to EventLoss [ i ], namely the OEP corresponding to the EventLoss [ i ], wherein the calculation formula is as follows:

6. and searching in the distributed OEP curve, and if the distributed OEP curve has the OEP value which is completely the same as the OEP value, taking the Loss value corresponding to the OEP value in the distributed OEP as the event adjusted Eventloss value. If the OEP value which is completely the same as the OEP value is not found, two OEP values which are the nearest to the distributed OEP are found out in the distributed OEP, and are respectively a smaller adjacent value OEPmin and a larger adjacent value OEPmax, meanwhile, the Loss corresponding to OEPmin in the distributed OEP is extracted and is recorded as Lossmin, the Loss corresponding to OEPmax is recorded as Lossmax, and the value of the event-adjusted EventLoss is calculated by a linear interpolation method according to OEPmin, Lossmin, OEPmax and Lossmax. The calculation formula is as follows:

implementations and functional operations of the subject matter described in this specification can be implemented in: digital electronic circuitry, tangibly embodied computer software or firmware, computer hardware, including the structures disclosed in this specification and their structural equivalents, or combinations of more than one of the foregoing. Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on one or more tangible, non-transitory program carriers, for execution by, or to control the operation of, data processing apparatus. The computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of one or more of the foregoing.

A computer program (which may also be referred to or described as a program, software application, module, software module, script, or code) can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data, e.g., one or more scripts stored in: in a markup language document; in a single file dedicated to the relevant program; or in multiple coordinated files, such as files that store one or more modules, sub programs, or portions of code. A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.

Computers suitable for carrying out computer programs include, and illustratively may be based on, general purpose microprocessors, or special purpose microprocessors, or both, or any other kind of central processing unit.

Implementations of the subject matter described in this specification can be implemented in a computing system that includes a back-end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front-end component, e.g., a client computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the subject matter described in this specification, or any combination of one or more such back-end, middleware, or front-end components. The components in the system can be interconnected by any form or medium of digital data communication, e.g., a communication network. Examples of communication networks include a local area network ("LAN") and a wide area network ("WAN"), e.g., the Internet. The computing system may include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.

While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any inventions or of what may be claimed, but rather as descriptions of features that may embody particular implementations of particular inventions. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in combination and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as: such operations are required to be performed in the particular order shown, or in sequential order, or all illustrated operations may be performed, in order to achieve desirable results. In certain situations, multitasking and parallel processing may be advantageous. Moreover, the separation of various system modules and components in the embodiments described above should not be understood as requiring such separation in all embodiments, and it should be understood that the program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

Particular embodiments of the subject matter have been described. Other implementations are within the scope of the following claims. For example, the activities recited in the claims can be performed in a different order and still achieve desirable results. As one example, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In certain implementations, multitasking and parallel processing may be advantageous.