Table Lookup Correction Method for Average Loss of Catastrophic Event Model

Abstract

The present invention relates to a table lookup correction method for the average loss of a catastrophe event model, including a parameter reading step, a table building step, a calculation step and a correction step; and a computer program product, wherein the computer program / instruction is executed by a processor to implement the technical solution of the present invention; and a computing system, wherein at least one processor and a memory storing instructions are provided, and when the instructions are executed by at least one processor, the technical solution of the present invention is implemented. The present invention specifically proposes a technical solution for generating a exceedance probability distribution table based on the ELT of the catastrophe event model, and by adjusting or correcting the average loss of the event with the help of the exceedance probability distribution table, the loss of the event can take into account the secondary uncertainty.

Description

Technical Field

[0001] The present invention relates to the field of reinsurance, and in particular to a table lookup correction method for average loss of a catastrophe event model. Background Art

[0002] In the process of calculating and pricing the losses of catastrophic events, the system first needs to simulate events based on the catastrophic model, that is, to generate the actual occurrence of catastrophic events. When simulating catastrophic events, the system will generate the actual occurrence of events YLT (Year Loss Table) based on the event information ELT (Event Loss Table) in the catastrophic model. Based on YLT, the system will calculate the exceedance probability curve OEP (Occurrence Exceedance Probability). OEP represents the probability OEP (X) that the loss of the event with the largest loss among the events that occur each year exceeds a certain value X.

[0003] When making the exceedance probability curve, only the average value of the loss was considered, without considering the uncertainty of the loss even if the event occurred. In other words, only the primary uncertainty (i.e. parameter risk) was considered, and the secondary uncertainty (i.e. process risk) was not considered. This will not be a big problem in the cumulative analysis of catastrophe risks by direct insurance companies. However, in the view of reinsurance companies, if they are doing excess compensation business, secondary uncertainty may have a certain impact on the valuation. This is mainly because if the average loss of an event is 9.9 million yuan, and the starting point of excess compensation is 10 million yuan, if the process risk is not considered at this time, the loss cost of excess compensation is zero. However, due to the existence of process risk, in fact, there is still a certain probability that the loss event will cause losses to excess compensation. Summary of the invention

[0004] In order to solve the above technical problems, the technical solution of the present invention proposes a table lookup correction method for the average loss of a catastrophic event model. The method corrects the average loss in the original catastrophic event model by establishing a exceedance probability distribution table taking into account the secondary uncertainty, comprising the following steps:

[0005] The parameter reading step reads ELT data of the catastrophe event model, wherein the ELT includes average loss;

[0006] The table building step builds a exceedance probability distribution table according to the ELT, wherein the exceedance probability distribution table includes a plurality of loss values ​​and an exceedance probability OEP corresponding to each of the loss values;

[0007] The calculation step calculates the exceedance probability according to the ELT;

[0008] The correction step compares each calculated exceedance probability with the exceedance probability in the distribution table, and corrects the loss value of the calculated exceedance probability by linear interpolation, replacing the average loss with the obtained corrected loss.

[0009] The present invention also provides a computer program product, including a computer program / instruction, which implements the technical solution of the present invention when executed by a processor.

[0010] The present invention also proposes a computing system, characterized in that the system includes at least one processor; and a memory storing instructions, which implement the technical solution of the present invention when the instructions are executed by the at least one processor.

[0011] The beneficial effect of the present invention is that it specifically proposes a technical solution for generating a exceedance probability distribution table based on the ELT of a catastrophic event model, and by adjusting or correcting the average loss of the event with the help of the exceedance probability distribution table, the loss of the event can take into account secondary uncertainty. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 , flow chart of the method for correcting the average loss of the lookup table catastrophic event model. DETAILED DESCRIPTION

[0013] The technical solution of the present invention is explained in detail below with reference to the accompanying drawings. In various implementations, the method of the present invention can be used as a preprocessing method for a catastrophic event loss risk model, such as Figure 1 As shown, the following steps are included:

[0014] The parameter reading step reads the ELT data of the catastrophe event model, where the ELT includes the average loss;

[0015] The table building step builds a exceedance probability distribution table according to the ELT, wherein the exceedance probability distribution table includes a plurality of loss values ​​and an exceedance probability OEP corresponding to each loss value;

[0016] Calculation steps: Calculate the exceedance probability according to ELT;

[0017] The correction step compares each calculated exceedance probability with the exceedance probability in the distribution table, and corrects the loss value of the calculated exceedance probability by linear interpolation, replacing the average loss with the obtained corrected loss.

[0018] Typically, each piece of information in the “ELT of the Catastrophe Event Model” (as shown in Table 1) includes information about an event, and each piece of information contains the following five fields:

[0019] 1. EventId: event identifier,

[0020] 2. EventFrequency: the annual frequency of the event,

[0021] 3. EventLoss: mean event loss,

[0022] 4. EventSTDV: standard deviation of the event loss,

[0023] 5. EventExposure: the maximum loss of an event;

[0024] Table 1. ELT of the catastrophe event model

[0025] EventId EventFrequency EventLoss EventSTDV EventExposure 10000 0.2 1500000 800000 5500000 20000 0.3 3000000 2000000 15000000 30000 0.4 6500000 5000000 50000000

[0026] The term “exceedance probability distribution table” is shown in Table 2, where the Loss column represents the loss value of the most costly event occurring each year, and the OEP column represents the probability that the loss value of the most costly event occurring in a year is greater than or equal to the Loss value.

[0027] Table 2. Exceedance probability distribution table

[0028] 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

[0029] The exceedance probability distribution table can be stored in a computer as a preset module. When executing the technical solution of the present invention, the data shown in Table 2 can be directly read.

[0030] In some implementations, the exceedance probability OEP corresponding to each loss value takes the frequency of occurrence of catastrophic events and the exceedance probability CEP corresponding to the loss value under the condition that only one catastrophic event occurs as parameters.

[0031] The annual occurrence of catastrophic events follows Poisson distribution. This implementation method includes a program implementation method that uses the transcendental function OEP as the main function.

[0032] In some implementation modes, the table building step specifically includes the following steps:

[0033] Sampling is performed within the range of the loss value L, and the OEP (L ≥ l) of each sampling point l where the loss value L is greater than or equal to the loss value L is calculated according to Formula I:

[0034] OEP(L≥l)=1-e -λ×CEP(L≥l) Formula I

[0035] Wherein, L is the loss value, l is the sampling point, OEP is the exceedance probability, OEP(L≥l) is the probability that the loss value L of the event is greater than or equal to the sampling point l; CEP is the exceedance probability under the condition that only one catastrophic event occurs, CEP(L≥l) is the probability that the loss value L is greater than or equal to the sampling point l under the condition that only one catastrophic event occurs; e is the natural base; λ is the total occurrence frequency of the simulated catastrophic event;

[0036] The exceedance probability OEP of each sampling point within the value range of L is recorded and stored as a table.

[0037] The loss value may range from 0 to infinity, or to a threshold that is large enough to prevent the occurrence of events with losses greater than the threshold.

[0038] “Sampling” includes taking a value according to a certain step frequency δ within the above value range, and taking the value as a sampling point.

[0039] CEP (conditional exceedance probability) is the probability that the loss value exceeds a certain value when only one catastrophic event occurs each year.

[0040] In some implementations, the loss value L is greater than or equal to the exceedance probability CEP (L ≥ l) under the condition that only one catastrophic event occurs at each sampling point l according to Formula II:

[0041]

[0042] Where L is the loss value, l is the sampling point, CEP(L≥l) is the probability that the loss value L is greater than or equal to the sampling point l under the condition that only one catastrophic event occurs; i is an integer ranging from 1 to n, and n is the number of catastrophic events simulated; EventFre i is the occurrence frequency of the ith simulated catastrophic event; Ps i (L≥l) is the survival function of the i-th simulated catastrophic event whose loss value is greater than or equal to the sampling point l.

[0043] In some embodiments, each Ps is calculated according to Formula III i (L≥l):

[0044]

[0045] Wherein, L is the loss value; i is an integer ranging from 1 to n, and n is the number of the simulated catastrophic events; Ps i (L≥l) is the survival function of the i-th simulated catastrophe event whose loss value is greater than or equal to the sampling point l; f i(x) is the probability density function that the loss value of the ith simulated catastrophic event is greater than or equal to the sampling point l.

[0046] The method for calculating the integral may adopt existing methods such as the trapz function and the Integral function of the MATLAB function library.

[0047] Some embodiments consider that the probability of each simulated catastrophic event follows a beta distribution, a normal distribution, a binomial distribution, or a log-binomial distribution.

[0048] Considering that the occurrence of different catastrophic events may obey different probability distribution models, the method of the present invention includes survival functions of different events obtained from different probability distribution models.

[0049] In some implementation methods, the probability distribution of the simulated catastrophic events all satisfies the beta distribution, and f in the above implementation methods is calculated according to Formula IV. i (x):

[0050]

[0051] Where i is an integer ranging from 1 to n, n is the number of catastrophic events simulated; f i (x) is the probability density function that the loss value of the i-th simulated catastrophic event is greater than or equal to the sampling point l; α is the first parameter of the probability distribution obeyed by the i-th simulated catastrophic event, and β is the second parameter of the probability distribution obeyed by the i-th simulated catastrophic event.

[0052] This embodiment considers the beta distribution as a distribution model with wider applicability.

[0053] In some embodiments, as a more specific step of the above embodiments, beta distribution parameters α and β are calculated according to Formula V and Formula VI, respectively:

[0054]

[0055]

[0056] Where i is an integer ranging from 1 to n, n is the number of simulated catastrophic events; α is the first parameter of the probability distribution obeyed by the i-th simulated catastrophic event, β is the second parameter of the probability distribution obeyed by the i-th simulated catastrophic event; Loss i is the average loss value of the ith simulated catastrophic event, Exp i is the maximum loss of the ith simulated catastrophe event; STDV i is the standard deviation of the loss of the ith simulated catastrophic event.

[0057] The variables in this embodiment can all be obtained from the ELT read in the parameter reading step.

[0058] In some more specific embodiments, the average loss can be calculated according to the following steps:

[0059] 1. Read the ELT data of the catastrophe event model;

[0060] 2. The OEP table directly generated by ELT in the above implementation is called distributed OEP and is stored in the computer as a preset module (or parameter);

[0061] Note: The distributed OEP curve results have taken into account the distribution characteristics and uncertainty of the event. After adjusting the loss of the event using the distributed OEP curve results, even if an event appears multiple times in the simulation results, the actual loss of each event is the same, which is the adjusted EventLoss value of the event. There is no need to sample each event multiple times, and after adjustment, the OEP results calculated by the system can be highly consistent with the distributedOEP results.

[0062] 3. Sort all events in ELT in descending order according to EventLoss. Assume that the loss of the i-th event after sorting is EventLoss[i], and the annual occurrence frequency of the i-th event is EventFrequency[i], i=1,2,…,n, where n is the number of events.

[0063] 4. For the i-th event, first calculate the sum of EventFrequency from the first event to the i-th event EventFrequencySum[i]. In the actual calculation process, EventFrequencySum[i] = EventFrequencySum[i-1] + EventFrequency;

[0064] Note: For the i-th event, the annual average probability of all events with losses greater than or equal to the event is the sum of the annual average probability of events with losses greater than the event and the annual average probability of the event. Since the events have been sorted from large to small according to EventLoss, the events with losses greater than or equal to the event are the 1st to the i-th events. The premise of this rule is that the distributed OEP is monotonic. In fact, the distributed OEP is monotonically decreasing. Since EventFrequencySum[i] must be greater than EventFrequencySum[i-1], the Loss of event i-1 is still greater than the Loss of event i after adjustment, so the magnitude relationship of event losses will not change due to adjustment.

[0065] 5. Calculate the probability that the annual maximum loss is greater than or equal to EventLoss[i], that is, the OEP corresponding to EventLoss[i]. The calculation formula is as follows:

[0066]

[0067] 6. Search in the distributed OEP curve. If there is an OEP value that is exactly the same as in the distributed OEP curve, take out the Loss value corresponding to the OEP value in the distributed OEP as the adjusted EventLoss value of the event. If the OEP value that is exactly the same as is not found, find the two OEP values ​​closest to in the distributed OEP, which are the smaller adjacent value OEPmin and the larger adjacent value OEPmax. At the same time, extract the Loss corresponding to OEPmin in the distributed OEP, recorded as Lossmin, and the Loss corresponding to OEPmax, recorded as Lossmax. Then the adjusted EventLoss value of the event is calculated based on , OEPmin, Lossmin, OEPmax, and Lossmax by linear interpolation. The calculation formula is as follows:

[0068]

[0069] The embodiments and functional operations of the subject matter described in this specification may be implemented in: digital electronic circuitry, tangibly implemented computer software or firmware, computer hardware, including the structures disclosed in this specification and their structural equivalents, or a combination of more than one of the above. The embodiments of the subject matter described in this specification may 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 a data processing device or for controlling the operation of a data processing device. 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 above.

[0070] A computer program (which may also be referred to or described as a program, software, software application, module, software module, script or code) may be written in any form of programming language, including compiled or interpreted languages ​​or declarative or procedural languages, and the computer program may 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 may be stored in a portion of a file that stores other programs or data, for example, one or more scripts stored in the following: in a markup language document; in a single file dedicated to a related program; or in multiple collaborative files, for example, files storing one or more modules, subroutines or code portions. A computer program may be deployed to execute on one or more computers, the computers being located in one place or distributed to multiple locations and interconnected by a communication network.

[0071] Computers suitable for the execution of a computer program may comprise, and by way of example may be based on, a general or special purpose microprocessor or both, or any other kind of central processing unit.

[0072] The embodiments of the subject matter described in this specification can be implemented in a computing system, which includes a back-end component such as a data server, or includes an intermediate component such as an application server, or includes a front-end component such as a client computer, which has a graphical user interface or a web browser, and a user can interact with the implementation of the subject matter described in this specification through a graphical user interface or a web browser, or the computer system includes any combination of one or more such back-end components, intermediate components or front-end components. The components in the system can be interconnected by digital data communication of any form or medium such as a communication network. Examples of communication networks include local area networks ("LANs") and wide area networks ("WANs"), for example, the Internet. The computing system can include a client and a server. The client and the server are usually far away from each other and usually interact through a communication network. The relationship between the client and the server is generated using a computer program that runs on each computer and has a client-server relationship between each other.

[0073] Although this specification contains many specific implementation details, these should not be interpreted as limitations on the scope of any invention or the scope of what can be claimed, but rather as an illustration of features that can concretize a particular embodiment of a particular invention. The specific features described in this specification in the context of independent embodiments can also be implemented in combination with a single embodiment. Conversely, the various features described in the context of a single embodiment can also be implemented independently in multiple embodiments, or in any suitable sub-combination. In addition, although the features can be described above as a combination effect and even initially required, one or more features from the required combination can be removed from the combination in some cases, and the required combination can be turned to a sub-combination or a variation of the sub-combination.

[0074] Similarly, although operations are described in the accompanying drawings in a particular order, it should not be understood that: in order to achieve the desired results, such operations are required to be performed in the particular order shown or in a sequential order, or that all illustrated operations are performed. In certain cases, multitasking and parallel processing can be advantageous. In addition, the separation of various system modules and components in the above-mentioned embodiments should not be understood as requiring such separation in all embodiments, and it should be understood that program components and systems can generally be integrated into a single software product or packaged into multiple software products.

[0075] Specific implementations 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 the desired results. As an example, the processes described in the accompanying drawings do not necessarily require the specific order or sequential order shown in order to achieve the desired results. In certain implementations, multitasking and parallel processing may be advantageous.

Claims

1. A table lookup correction method for average loss of a catastrophic event model, characterized in that: The following steps are involved: The parameter reading step reads the ELT data of the catastrophe event model, wherein the ELT includes the average loss; the table building step builds a exceedance probability distribution table according to the ELT, wherein the exceedance probability distribution table includes a number of loss values ​​and an exceedance probability OEP corresponding to each of the loss values; The calculation step calculates the exceedance probability according to the ELT; The correction step compares each calculated exceedance probability with the exceedance probability in the distribution table, and corrects the loss value of the calculated exceedance probability by linear interpolation, replacing the average loss with the corrected loss; The exceedance probability OEP corresponding to each loss value is calculated with the occurrence frequency of catastrophic events and the exceedance probability CEP under the condition that only one catastrophic event occurs corresponding to the loss value as parameters; the table building step specifically includes the following steps: Sampling is performed within the range of the loss value L, and the OEP (L ≥ l) of each sampling point l where the loss value L is greater than or equal to the loss value L is calculated according to Formula I: OEP(L≥l)=1-e -λ×CEP(L≥l) Formula I Wherein, L is the loss value, l is the sampling point, OEP is the exceedance probability, OEP(L≥l) is the probability that the loss value L is greater than or equal to the sampling point l; CEP is the exceedance probability under the condition that only one catastrophic event occurs, CEP(L≥l) is the probability that the loss value L is greater than or equal to the sampling point l under the condition that only one catastrophic event occurs; e is the natural base; λ is the total occurrence frequency of the simulated catastrophic event; Record the exceedance probability OEP of each sampling point within the value range of L and store it as a table; According to Formula II, the exceedance probability CEP (L ≥ l) under the condition that the loss value L is greater than or equal to each sampling point l and only one catastrophic event occurs is calculated: Where L is the loss value, l is the sampling point, CEP(L≥l) is the probability that the loss value L is greater than or equal to the sampling point l under the condition that only one catastrophic event occurs; i is an integer ranging from 1 to n, and n is the number of catastrophic events simulated; EventFre i is the occurrence frequency of the ith simulated catastrophic event; Ps i (L≥l) is the survival function of the i-th simulated catastrophe event whose loss value is greater than or equal to the sampling point l; Calculate each of the Ps according to Formula III i (L≥l): Wherein, L is the loss value; i is an integer ranging from 1 to n, and n is the number of the simulated catastrophic events; Ps i (L≥l) is the survival function of the i-th simulated catastrophe event whose loss value is greater than or equal to the sampling point l; f i (x) is the probability density function of the i-th simulated catastrophe event loss value being greater than or equal to the sampling point l; Calculate each of the f according to Formula IV i (x): Wherein, i is an integer ranging from 1 to n, and n is the number of the simulated catastrophic events; f i (x) is the probability density function that the loss value of the i-th simulated catastrophic event is greater than or equal to the sampling point l; α is the first parameter of the probability distribution obeyed by the i-th simulated catastrophic event, and β is the second parameter of the probability distribution obeyed by the i-th simulated catastrophic event.

2. The method according to claim 1, characterized in that The probability of each simulated catastrophic event follows a beta distribution, a normal distribution, a binomial distribution, or a log-binomial distribution.

3. The method according to claim 1, characterized in that The α and β are calculated according to Formula V and Formula VI, respectively: Wherein, i is an integer ranging from 1 to n, and n is the number of the simulated catastrophic events; α is the first parameter of the probability distribution obeyed by the i-th simulated catastrophic event, and β is the second parameter of the probability distribution obeyed by the i-th simulated catastrophic event; Loss i is the average loss value of the ith simulated catastrophic event, Exp i is the maximum loss of the ith simulated catastrophe event; STDV i is the standard deviation of the loss of the ith simulated catastrophic event.

4. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the method according to claims 1-3 are implemented.

5. A computing system, characterized in that: The system comprises at least one processor; and a memory storing instructions, and when the instructions are executed by the at least one processor, the steps of the method according to any one of claims 1 to 3 are implemented.

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