A method for correcting the average loss of catastrophic event models

Abstract

The present invention relates to a method for correcting the average loss of a catastrophic event model, comprising the following steps: a parameter reading step of reading the event identifier of each catastrophic event and the corresponding average loss and annual frequency of occurrence, and reading a preset exceedance probability and a corresponding preset loss value; a calculation step of calculating the exceedance probability of each average loss based on the annual frequency of occurrence of each catastrophic event; a search step of comparing the exceedance probability of each average loss with the preset exceedance probability, and searching for a value in the preset exceedance probability that is the same as the exceedance probability of the average loss; and a replacement step of replacing the average loss with a value in the preset exceedance probability that is the same as the exceedance probability of the average loss as the correction loss. According to the technical solution of the present invention, it is not necessary to perform multiple sampling operations on the probability distribution of event occurrence, and at the same time, it can ensure that the generated exceedance probability curve has good accuracy and stability.

Description

Technical Field

[0001] The present invention relates to the field of reinsurance, and in particular to a method for correcting average losses of a catastrophic event model. Background Art

[0002] During the catastrophic event loss calculation and pricing process, the system first simulates events based on the catastrophic model, essentially generating actual catastrophic event scenarios. During catastrophic event simulation, the system generates actual event scenarios based on the event information in the catastrophic model. After simulating and generating the actual event scenarios, the system generates the actual losses for each actual event. To generate the actual losses, the system constructs a probability distribution for the event, followed by simulated sampling.

[0003] If an event occurs frequently in the simulation results, the distribution of that event must be sampled the same number of times. This sampling operation takes a long time. Since the total number of events is in the tens of millions, a 100,000-year simulation would produce hundreds of millions of events in the resulting table of actual occurrences. Therefore, hundreds of millions of sampling operations would be required, necessitating a significant computational effort.

[0004] Furthermore, if an event actually occurs only a few times, such as just once, then sampling results will be difficult to accurately represent the loss distribution of that event. Each calculation will yield different results. Consequently, when subsequently calculating the probability of exceedance (OEP), the calculated annual maximum loss for the corresponding probability will fluctuate significantly, affecting the accuracy and stability of the results. Summary of the Invention

[0005] To solve the above technical problems, the present invention proposes a method for adjusting the average loss of a catastrophic event model, comprising the following steps:

[0006] The parameter reading step reads the event identifier of each catastrophic event and the corresponding average loss and annual frequency of occurrence, and reads the preset exceedance probability and the corresponding preset loss value;

[0007] The calculation step calculates the exceedance probability of each of the average losses based on the annual occurrence frequency of each catastrophic event;

[0008] The searching step compares the exceedance probability of each of the average losses with the preset exceedance probability, and searches for a value in the preset exceedance probability that is the same as the exceedance probability of the average loss;

[0009] The replacing step replaces the average loss with a value of the preset exceedance probability that is the same as the exceedance probability of the average loss as the correction loss.

[0010] The present invention also provides a computer program product, comprising a computer program, which implements the technical solution of the present invention when executed by a processor.

[0011] The present invention also proposes a correction device for the average loss of a catastrophic event model, comprising at least one processor and a memory storing instructions. When the instructions are executed by the at least one processor, the technical solution of the present invention is implemented.

[0012] The exceedance probability (curve) can be generated entirely according to a specific method based on the catastrophic event model. The average loss of the event is then adjusted or corrected with the help of the exceedance probability (curve), so that the loss of the event can take into account the quadratic uncertainty. Therefore, when the system determines the actual loss of the event, it can simulate the adjusted or corrected loss value. According to the technical solution of the present invention, the actual loss of each event is the same, so there is no need to perform multiple sampling operations on the probability distribution of the event, and at the same time, it can ensure that the generated exceedance probability curve has good accuracy and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 , flow chart of the correction method for average loss of catastrophic event model. DETAILED DESCRIPTION

[0014] In various embodiments, the methods of the present invention are Figure 1 As shown, the following steps are included:

[0015] The parameter reading step reads the event identifier of each catastrophic event and the corresponding average loss and annual frequency of occurrence, and reads the preset exceedance probability and the corresponding preset loss value;

[0016] The calculation step calculates the exceedance probability of each of the average losses based on the annual occurrence frequency of each catastrophic event;

[0017] The searching step compares the exceedance probability of each of the average losses with the preset exceedance probability, and searches for a value in the preset exceedance probability that is the same as the exceedance probability of the average loss;

[0018] The replacing step replaces the average loss with a value of the preset exceedance probability that is the same as the exceedance probability of the average loss as the correction loss.

[0019] Typically, each piece of information in the "catastrophic event model" (as shown in Table 1) includes information about an event, and each piece of information contains the following five fields:

[0020] 1. EventId: event identifier,

[0021] 2. EventFrequency: the annual frequency of the event,

[0022] 3. EventLoss: mean event loss,

[0023] 4. EventSTDV: standard deviation of event loss,

[0024] 5. EventExposure: The maximum loss of the event;

[0025] Table 1. Catastrophic event model

[0026] EventId EventFrequency EventLoss EventSTDV EventExposure 10000 0.2 1500000 800000 5500000 20000 0.3 3000000 2000000 15000000 30000 0.4 6500000 5000000 50000000

[0027] The term "preset exceedance probability" 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.

[0028] Table 2. Exceedance probability function table

[0029] 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

[0030] The preset exceedance probability is calculated based on the ELT using a statistical method and stored in the computer as a preset module. When executing the technical solution of the present invention, the data shown in Table 2 can be directly read.

[0031] In some embodiments, the exceedance probability derived from the "Re-Type" of China Re Group can be used as the preset exceedance probability of the technical solution of the present invention.

[0032] The present invention adjusts or corrects the average losses of existing catastrophic event models, generating an adjusted or corrected catastrophic event model table for use in catastrophic event simulations. During catastrophic event simulations, the system generates actual event scenarios based on this adjusted or corrected catastrophic event model. The simulation results are output as a yearly loss table (YLT) (as shown in Table 3).

[0033] Table 3. Annual losses

[0034]

[0035]

[0036] In some embodiments, the exceedance probability of each of the average losses is calculated according to Formula 1:

[0037]

[0038] Among them, OEP(EventLoss[i]) represents the exceedance probability of the i-th average loss, EventLoss[i] represents the i-th average loss in the sorted average loss, EventFrequencySum[i] represents the i-th cumulative frequency, and e is the natural bottom.

[0039] In ELT, the annual number of occurrences of each event follows a Poisson distribution, whose parameter λ is the frequency of the event. Since the Poisson distribution is additive, the annual number of occurrences of multiple events in ELT follows a Poisson distribution whose parameter is the sum of the frequencies of the events. For a point in the exceedance probability (OEP), the loss value (Loss) at that point must be the actual loss of a certain event (assuming it's EventA) after accounting for quadratic uncertainty. The frequency (Frequency) is the probability that the loss of the event with the highest loss in a year is greater than or equal to the loss. In other words, the probability that at least one of EventA and all events with greater losses than EventA will occur in a year. Assuming the sum of the frequencies of these events is FrequencySum, the OEP value is calculated as follows:

[0040]

[0041] In some embodiments, the following steps are further included:

[0042] Sort the catastrophic events by their average loss size to obtain the corresponding sorted average loss and sorted annual frequency;

[0043] The frequency of occurrence of the sorted years is accumulated in sequence to obtain the cumulative frequency.

[0044] In some embodiments, if the exceedance probability function table does not contain a value identical to the exceedance probability of the average loss, the two values ​​in the exceedance probability function table closest to the exceedance probability of the average loss are used to perform linear interpolation calculation according to Formula II to obtain the simulated loss:

[0045]

[0046] Among them, Loss[i] represents the simulated loss of the i-th event, EventLoss[i] represents the i-th average loss, OEP(EventLoss[i]) represents the exceedance probability of the i-th average loss, OEPmin represents the smaller of the two values ​​closest to the EventLoss[i] in the function table, Lossmin is the loss value corresponding to OEPmin, OEPmax represents the larger of the two values ​​closest to the EventLoss[i] in the function table, and Lossmax is the loss value corresponding to OEPmax.

[0047] In some embodiments, if there is only one OEPmin (or one OEPmax) value closest to the exceedance probability OEP (EventLoss[i]) of a certain average loss in the exceedance probability function table, the Lossmin corresponding to the OEPmin (or the Lossmax corresponding to the OEPmax) is the simulated loss Loss[i] of this average loss.

[0048] This embodiment is an embodiment in which the interpolation node is at an endpoint in the above-mentioned embodiment.

[0049] In some embodiments, the cumulative frequency is calculated according to Formula III:

[0050] EventFrequencySum[i]=EventFrequencySum[i-1]+EventFrequency[i] Formula III

[0051] Among them, EventFrequencySum[i] represents the i-th cumulative frequency, and EventFrequency[i] represents the i-th annual occurrence frequency in the sorted annual occurrence frequency.

[0052] In some embodiments, if the preset exceedance probability does not have a value that is the same as the exceedance probability of the average loss, the correction loss can be calculated by Lagrange interpolation using N values ​​of the preset exceedance probability.

[0053] This embodiment is an alternative to the linear interpolation method. Preferably, N is greater than 2.

[0054] In some more specific embodiments, the prior art used as a comparative example uses the original ELT1 to generate the annual loss table YLT, in which the event loss EventLoss is the average loss of the event. However, the actual loss of the event after simulation may not be equal to EventLoss. Generally, the system simulates each event into a Beta distribution (or other probability distribution, such as normal distribution, binomial distribution, uniform distribution, etc.) with a mean of EventLoss and a standard deviation of EventSTDV, and then performs a specified number of samplings based on the occurrence of the event to obtain the actual loss at each event. For example, event 10000 occurs twice in 10 years. Therefore, when determining the actual loss of the event, event 10000 needs to be constructed as a Beta distribution with a mean of 1500000 and an EventSTDV of 800000, and then performs two random samplings to obtain the actual losses of the two events to form YLT.

[0055] If an event occurs frequently in the simulation results, the distribution of that event must be sampled the same number of times. This sampling operation takes a long time. Due to the large number of events in ELT, which total tens of millions, and the system running a 100,000-year simulation, the number of simulated events will reach hundreds of millions, requiring hundreds of millions of sampling cycles. Furthermore, sampling must be performed during every business calculation, significantly slowing down the calculation process.

[0056] Furthermore, if an event occurs only a few times, such as just once, the sampling results will be difficult to accurately represent the loss distribution of that event. Each calculation will yield different results. Consequently, when subsequently calculating the probability of exceedance (OEP), the calculated annual maximum loss for the corresponding probability will fluctuate significantly, affecting the accuracy and stability of the results.

[0057] When determining the actual loss of an event, the system can adjust the loss of the event through the OEP curve generated by ELT. After using this method, the actual loss of the event is the same every time it occurs, so there is no need to perform multiple sampling operations like Beta sampling, but at the same time it can ensure that the generated OEP curve has good accuracy and stability.

[0058] Using a specified method such as the "Re-Type" independently developed by China Re Group, or the RMSRisk Intelligence (RI), a cloud platform of the RMS risk management system, the OEP curve is directly generated through ELT, which is called distributed OEP. Then, the EventLoss of the event is adjusted with the help of the distributed OEP curve, so that the actual loss of the event can take into account the quadratic uncertainty. The distributed OEP curve result has already taken into account the distribution characteristics and uncertainty of the event. After adjusting the loss of the event using the distributed OEP curve result, although a certain 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 the adjustment, the OEP result calculated by the system can be highly consistent with the distributedOEP result. The adjustment steps are as follows:

[0059] 1. Sort all events in the 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.

[0060] 2. 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;

[0061] Note: For the i-th event, the average annual probability of all events with losses greater than or equal to the event is the sum of the average annual probability of events with losses greater than the event and the average annual probability of the event itself. Since events are sorted from largest to smallest by EventLoss, the events with losses greater than or equal to the event are events 1 to ith. This rule assumes that the distributed OEP is monotonic. In fact, the distributed OEP is monotonically decreasing. Since EventFrequencySum[i] is always greater than EventFrequencySum[i-1], the loss of event i-1 remains greater than the loss of event i after adjustment. Therefore, the relationship between event losses does not change due to the adjustment.

[0062] 3. Calculate the probability that the maximum annual loss is greater than or equal to EventLoss[i], which is the OEP corresponding to EventLoss[i]. The calculation formula is as follows:

[0063]

[0064] 4. Search in the distributed OEP curve. If there is an OEP value exactly the same as the event 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 no OEP value exactly the same as the event is found, find the two closest OEP values ​​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. 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:

[0065]

[0066] In order to prove that this solution can save calculation time and the obtained exceedance probability OEP curve has good accuracy and stability, the technical solution of the present invention is used to calculate an actual business and a business combination, and the calculation speed and calculation results are examined.

[0067] First, let's compare the calculation speed and results of an actual business. When calculating the loss of this business, this experiment used the Beta distribution sampling method and the method used in this invention to perform the calculation. The calculation time is as follows:

[0068] Beta Sampling Method Lookup table method 32.5S 17.4S

[0069] The OEP results calculated using the two methods are as follows:

[0070]

[0071]

[0072] Next, this experiment compares the calculation speed and results of a business combination. When calculating the loss of this business, this experiment uses the Beta distribution sampling method and the method used in this invention to perform the calculation. The calculation time is as follows:

[0073] Beta Sampling Method Lookup table method 40min 17min

[0074] The OEP results calculated using the two methods are as follows:

[0075] Return period (years) Beta Sampling Method Lookup table method 10000 5,099,369 5,099,245 5000 5,068,946 5,069,786 1000 5,000,000 5,000,000 500 5,000,000 5,000,000 250 5,000,000 5,000,000 200 5,000,000 5,000,000 100 4,755,113 4,897,769 50 4,698,834 4,717,944 25 3,764,398 3,808,530 10 2,590,321 2,598,438 5 2,000,000 2,000,000 2 689,680 696,171

[0076] The implementation and functional operations of the subject matter described in this specification can be implemented using: 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 one or more of the foregoing. The implementation 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, a data processing apparatus.

[0077] 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 as part of a file that stores other programs or data, for example, as one or more scripts in a markup language document, in a single file dedicated to the program in question, or in multiple collaborative files, for example, files storing one or more modules, subroutines, or portions of code. A computer program may be deployed to execute on one or more computers, located in one location or distributed across multiple locations and interconnected by a communications network.

[0078] The processes and logic flows described in this specification can be performed by one or more programmable computers that execute one or more computer programs to perform functions by operating on input data and generating output. Computers suitable for executing computer programs include and can be based, for example, on general-purpose microprocessors or special-purpose microprocessors or both, or any other type of central processing unit. Computer-readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media, and storage devices.

[0079] Although this specification contains many specific implementation details, these should not be interpreted as limitations on the scope of any invention or on the scope of what can be claimed, but rather as illustrations of features that can concretize a particular embodiment of a particular invention. Specific features described in this specification in the context of independent embodiments can also be implemented in combination with a single embodiment. Conversely, 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 features may be described above as acting in combination and even initially claimed as such, one or more features from a claimed combination may in some cases be removed from the combination, and a claimed combination may be turned into a sub-combination or a variation of a sub-combination.

[0080] 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 must be performed in the particular order shown or in sequential order, or that all illustrated operations must be performed. In certain circumstances, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system modules and components in the above-described 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.

[0081] While certain embodiments of the subject matter have been described, other embodiments 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. In certain implementations, multitasking and parallel processing may be advantageous.

Claims

1. A method for correcting the average loss of a catastrophic event model, characterized in that: The following steps are involved: The parameter reading step reads the event identifier of each catastrophic event and the corresponding average loss and annual frequency of occurrence, and reads the preset exceedance probability and the corresponding preset loss value; The calculation step calculates the exceedance probability of each of the average losses based on the annual occurrence frequency of each catastrophic event; The searching step compares the exceedance probability of each of the average losses with the preset exceedance probability, and searches for a value in the preset exceedance probability that is the same as the exceedance probability of the average loss; The replacing step replaces the average loss with a value of the preset exceedance probability that is the same as the exceedance probability of the average loss as the correction loss; The exceedance probability of each of the average losses is calculated according to Formula 1: Among them, OEP(EventLoss[i]) represents the exceedance probability of the i-th average loss, EventLoss[i] represents the i-th average loss in the sorted average loss, EventFrequencySum[i] represents the i-th cumulative frequency, and e is the natural bottom; If there is no value in the preset exceedance probabilities that is the same as the exceedance probability of the average loss, the correction loss is calculated by Lagrange interpolation using N values ​​in the preset exceedance probabilities, where N is greater than 2.

2. The method according to claim 1, wherein The following steps are also included: Sorting the catastrophic events according to the average loss size to obtain the corresponding sorted average loss and sorted annual occurrence frequency; The occurrence frequencies of the sorted years are accumulated in sequence to obtain the accumulated frequency.

3. The method according to claim 2, wherein If there is no value in the preset exceedance probabilities that is the same as the exceedance probability of a certain average loss, the correction loss is calculated by linear interpolation using the two values ​​in the preset exceedance probabilities that are closest to the exceedance probability according to Formula II: Wherein, Loss[i] represents the corrected loss of the i-th catastrophic event, EventLoss[i] represents the i-th average loss in the sorted average loss, OEP(EventLoss[i]) represents the exceedance probability of EventLoss[i], OEPmin represents the smaller of the two values ​​closest to EventLoss[i] in the preset exceedance probability, Lossmin is the loss value corresponding to OEPmin, OEPmax represents the larger of the two values ​​closest to EventLoss[i] in the preset exceedance probability, and Lossmax is the loss value corresponding to OEPmax.

4. The method according to claim 3, wherein If the value closest to the exceedance probability OEP(EventLoss[i]) of a certain average loss among the preset exceedance probabilities is only OEPmin, the Lossmin corresponding to the OEPmin is the corrected loss Loss[i] of the average loss.

5. The method according to claim 3, wherein If the value closest to the exceedance probability OEP(EventLoss[i]) of a certain average loss among the preset exceedance probabilities is only OEPmax, the Lossmax corresponding to the OEPmax is the corrected loss Loss[i] of the average loss.

6. The method according to claim 4, wherein The cumulative frequency is calculated according to formula III: EventFrequencySum[i]=EventFrequencySum[i-1]+EventFrequency[i] Formula III Among them, EventFrequencySum[i] represents the i-th cumulative frequency, and EventFrequency[i] represents the i-th annual occurrence frequency in the sorted annual occurrence frequency.

7. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of any one of the methods described in claims 1 to 6 are implemented.

8. A device for adjusting the average loss of a catastrophic event model, 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 any one of the methods according to any one of claims 1 to 6 are implemented.

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