Abstract:
Systems and methods of the present technology provide the capability to determine risk exposure of points of interest (e.g., insured locations) based on the occurrence of an event (e.g., a catastrophic event). The systems and methods use two-dimensional convolution and FFT processing to provide quick determinations.

Description:
FIELD OF THE INVENTION 
       [0001]    The present technology relates to systems and methods for determining risk exposure of points of interest such as e.g., insured locations based on the occurrence of an event (e.g., a catastrophic event). 
       DESCRIPTION OF RELATED ART 
       [0002]    It is known that models or other computer applications may be used to assess the potential liabilities of catastrophic events. These events may be either man-made (e.g., terrorist attack) or naturally occurring disasters such as e.g., earthquakes, tornados, and hurricanes. 
         [0003]    Certain companies, such as insurance companies, may find information provided by these models/applications useful in determining their potential liability (i.e., risk exposure) based on the occurrence of the event. These models/applications use, generate and store large amounts of data that need to be processed and analyzed to facilitate the determination of its potential liabilities based on the event. The existing methods are also time consuming. As such, there is a need and desire for a better system and method for determining risk exposure of e.g., insured locations based on the occurrence of an event such as a catastrophic event. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0004]    Specific examples have been chosen for purposes of illustration and description, and are shown in the accompanying drawings, forming a part of the specification. 
           [0005]      FIG. 1  illustrates one example of a computing device system of the present technology. 
           [0006]      FIG. 2  illustrates one example of points of interest illustrated with an overlying grid. 
           [0007]      FIG. 3  illustrates one example of a grid with cells containing exposure summations based on the points of interest illustrated in  FIG. 2 . 
           [0008]      FIG. 4  illustrates an example event footprint superimposed over a footprint grid. 
           [0009]      FIG. 5  illustrates an example of shape coverage factors for the cells within the footprint grid illustrated in  FIG. 4 . 
           [0010]      FIG. 6  illustrates an example data grid having an apron comprising kernel padding cells around the insured location grid of  FIG. 3 , and example anchoring techniques for a kernel. 
           [0011]      FIG. 7  illustrates an example grid having cells filled with convolution results. 
       
    
    
     DETAILED DESCRIPTION 
       [0012]    The technology disclosed herein provides the capability to determine risk exposure or other statistical or characteristics of “points of interest” (e.g., insured locations) when the points of interest have been exposed to an event such as e.g., a catastrophic event that triggers insurance coverage. One existing application for determining risk exposure places a given set of insured locations on a map and creates a spatial “footprint” of the event. The footprint has a certain shape (i.e., polygon) and size based on the event. The application then uses the footprint and the map to determine the insured locations with the largest amount of exposure (i.e., locations covered by the footprint having the most liability for the insurance carrier). 
         [0013]    The application associates a grid of cells with the map of insured risks, and partitions the insured locations into different grid cells. The grid cells are set to a specified width and height based on latitude and longitude, and the insured locations within each of the cells are identified. The spatial footprint of the event is also partitioned into a grid having the same resolution as the map&#39;s grid. Using a process based on an SQL database, the intersection of the spatial footprint grid cells and the insured locations&#39; grid cells is calculated. The spatial footprint is moved across the grid of insured locations and anchored at various locations along the map grid. Exposure of map grid cells covered by the spatial footprint is then calculated. By comparing the aggregations from each anchor point, one could identify the anchor points where the exposure was at its highest values. It should be appreciated that the principles disclosed herein can do more than identifying the highest exposure values; for example, the disclosed principles provide the ability to identify the whole range of exposure values (e.g., all anchor points greater than one billion dollars, two billion dollars, etc.). This whole distribution is then a key factor in determining the exceedance probability (EP) distribution of potential losses. 
         [0014]    One major shortcoming of the current approach is that it takes a long time to run its analysis. As can be appreciated, this shortcoming is very undesirable and needs to be addressed. 
         [0015]    The inventors have determined that the risk exposure determining process could be performed in a different and much more beneficial manner using a process known as convolution or moving window analysis. As is known in the art, convolution is a processing technique that takes a kernel of coefficients or weights (usually a matrix) and applies it to a set of points (e.g., pixels in an image) to calculate values for each point. The value for a point typically includes multiplying the point and its neighbors with the coefficients/weights in the kernel. The sum of the multiplications are added and stored as that point&#39;s value. 
         [0016]    In the disclosed convolution risk exposure determination technique, points of interest (e.g., insured locations) are represented by a first grid, referred to herein as the insured location grid for convenience purposes only. In addition, the event footprint will be represented by a second grid, referred to herein as the spatial footprint grid for convenience purposes only. As will become apparent, the grids will be used to create a spatial footprint kernel (discussed below in more detail) that is then used in a moving window analysis to generate values of risk exposure for each insured location within the first grid. A final determination for where the risk exposure is the greatest can be made from the risk exposure values for each location. 
         [0017]    Various examples of the present technology may be implemented with computing device devices, computing device networks and systems that exchange and present information. Elements of an exemplary computing device system are illustrated in  FIG. 1 , in which the convolution risk exposure determination functionality are provided to a user by a computing device  100 . Computing device  100  can be connected to a local area network (LAN)  102  and/or a wide area network (WAN)  104 . Computing device  100  can include a central processor  110  that controls the overall operation of the computing device, and a system bus  112  that connects central processor  110  to the components described below. System bus  112  may be implemented with any one of a variety of conventional bus architectures. 
         [0018]    Computing device  100  can include a variety of interface units and drives for reading and writing data or files. In particular, computing device  100  can include a local memory interface  114  and a removable memory interface  116  respectively coupling a hard disk drive  118  and a removable memory drive  120  to system bus  112 . Examples of removable memory drives include magnetic disk drives and optical disk drives that receive removable memory elements  122 . Hard disks generally include one or more read/write heads that convert bits to magnetic pulses when writing to a computing device-readable medium and magnetic pulses to, bits when reading data from the computing device readable medium. A single hard disk drive  118  and a single removable memory drive  120  are shown for illustration purposes only and with the understanding that computing device  100  may include several of such drives. Furthermore, computing device  100  may include drives for interfacing with other types of computing device readable media such as magneto-optical drives. 
         [0019]    Unlike hard disks, system memories, such as system memory  120 , generally read and write data electronically and do not include read/write heads. System memory  120  may be implemented with a conventional system memory having a read only memory section that stores a basic input/output system (BIOS) and a random access memory (RAM) that stores other data and files. 
         [0020]    A user can interact with computing device  100  with a variety of input devices, and through graphical user interfaces provided to the user by the computing device  100 , such as though a browser application. For example,  FIG. 1  shows a universal serial bus (USB) interface  122  coupling a keyboard  124  and a pointing device  126  to system bus  112 . Pointing device  132  may be implemented with a hard-wired or wireless mouse, track ball, pen device, or similar device. 
         [0021]    Computing device  100  may include additional interfaces for connecting peripheral devices to system bus  112 .  FIG. 1  shows a IEEE 1394 interface  128  that may be used to couple additional devices to computing device  100 . Peripheral devices may include game pads scanners, printers, and other input and output devices and may be coupled to system bus  112  through parallel ports, game ports, PCI boards or any other interface used to couple peripheral devices to a computing device. 
         [0022]    Computing device  100  also includes a video adapter  130  coupling a display device  132  to system bus  112 . Display device  132  may include a cathode ray tube (CRT), liquid crystal display (LCD), field emission display (FED), plasma display or any other device that produces an image that is viewable by the user. A touchscreen interface  134  may be included to couple a touchscreen (not shown) to system buss  112 . A touchscreen may overlay at least part of the display region of display device  132  and may be implemented with a convention touchscreen technology, such as capacitive or resistive touchscreen technology. 
         [0023]    One skilled in the art will appreciate that the device connections shown in  FIG. 1  are for illustration purposes only and that several of the peripheral devices could be coupled to system bus  112  via alternative interfaces. For example, a video camera could be connected to IEEE 1394 interface  128  and pointing device  126  could be connected to another interface. 
         [0024]    Computing device  100  may include a network interface  136  that couples system bus  112  to LAN  102 . LAN  102  may have one or more of the well-known LAN topologies and may use a variety of different protocols, such as Ethernet. Computing device  100  may communicate with other computing devices and devices connected to LAN  102 , such as computing device  138  and printer  140 . Computing devices and other devices may be connected to LAN  102  via twisted pair wires, coaxial cable, fiber optics or other media. Alternatively, electromagnetic waves, such as radio frequency waves, may be used to connect one or more computing devices or devices to LAN  102 . 
         [0025]    A wide area network  104 , such as the Internet, can also be accessed by computing device  100 .  FIG. 1  shows network interface  136  connected to LAN  102 . LAN  102  may be used to connect to WAN  104 .  FIG. 1  shows a router  142  that may connect LAN  102  to WAN  104  in a conventional manner. A server  144 . Mobile terminal  146  and a computing device  148  are shown connected to WAN  104 . Of course, numerous additional servers, computing devices, handheld devices, personal digital assistants, telephones and other devices may also be connected to WAN  104 . 
         [0026]    In some examples, a mobile network card  150  may be used to connect to LAN  102  and/or WAN  104 . Mobile network card may be configured to connect to LAN  102  and/or WAN  104  via a mobile telephone network in a conventional manner. 
         [0027]    The operation of computing device  100  and server  144  may be controlled by computing device-executable instructions stored on a non-transient computing device-readable medium. For example, computing device  100  may include computing device-executable instructions stored on a memory for transmitting information to server  144 , receiving information from server  144  and displaying the received information on display device  132 . Furthermore, server  144  may include stored on a memory computing device-executable instructions for, receiving requests from computing device  100 , processing data and transmitting data to computing device  100 . In some embodiments server  144  transmits hypertext markup language (HTML) and extensible markup language (XML) formatted data to computing device  100 . 
         [0028]    As noted above, the term “network” as used herein and depicted in the drawings should be broadly interpreted to include not only systems in which remote storage devices are coupled together via one or more communication paths, but also stand-alone devices that may be coupled, from time to time, to such systems that have storage capability. Consequently, the term “network” includes not only a “physical network”  102  and  104 , but also a “content network,” which is comprised of the data—attributable to a single entity—which resides across all physical networks. 
         [0029]    An example of the disclosed convolution risk exposure determination is now described with reference to  FIGS. 2-7 .  FIG. 2  illustrates one example of points of interest P1, P2, Pn illustrated with an overlying grid  200 . In the present example, the points of interest P1, P2, . . . Pn are insured locations within a region associated with the grid  200  and each insured location is associated with a particular amount of insurance coverage (i.e., risk exposure). In the illustrated embodiment, each point of interest P1, P2, Pn corresponds to $100,000 of exposure. It should be appreciated that this is an example amount of exposure and that any amount could be used. The grid  200  contains an array of cells C1, . . . , Cn, which can be configured/sized to represent regions of interest (e.g., specific cities, regions on a map, etc.). It is desirable for the grid to be tight enough to capture the exposure distribution on the scale of a tornado. Tornado tracks range in length from less than a mile to over fifty miles and are up to one mile wide. Therefore, in one embodiment, the grid  200  resolution is one mile-by-one mile or smaller. It should be appreciated that the grid  200  can have more or less rows/columns than those illustrated and that the disclosed embodiment is not to be limited to any particular grid size. In one embodiment, the preparation of the insured location grid  200  is done at runtime—rather than beforehand—which allows for the flexibility of filtering the data for various criteria, allows for flexibility of the grid resolution, eliminates the manual process of creating the grid, and eliminates the storage requirements for the grid and any intermediate results. In one embodiment, the grid can be generated at runtime from a SQL database of stored, geocoded locations. By scaling and rounding the geocoded latitude and longitude appropriately, a new grid can be produced very efficiently as a table, which can then be transformed into matrix form. 
         [0030]      FIG. 3  illustrates one example of the grid  200  with cells C1, . . . , Cn containing exposure summations S1, . . . , Sn based on the points of interest P1, P2, . . . Pn illustrated in  FIG. 2 . In the illustrated example, the first cell C1 has a summation S1 of $200,000 based on the summation of the exposures of points P1 and P2. It should be appreciated that the contents of the cells are not limited to summations and could, alternatively or additionally, include other mathematical operations or relationships of the data and/or other statistical data if desired. 
         [0031]      FIG. 4  illustrates an example event footprint  300  superimposed over a footprint grid  400 . In the illustrated example, the footprint  300  is shown as being a circle, but it should be appreciated that any shape (e.g., square, rectangle, polygon, etc.) can be used to represent the footprint of the event. Moreover, the footprint could actually be a set of nested polygons, so that a different percentage of the exposed risks located within each polygon could contribute to the aggregate total. The footprint grid  400  comprises an array of footprint cells FC1, . . . , FCm. The footprint cells FC1, . . . , FCm have the same size (i.e., dimensions) as the insured location cells C1, . . . , Cn illustrated in  FIGS. 2 and 3 . In the illustrated embodiment, the grid  400  comprises a 3×3 array of footprint cells FC1, FCm. It should be appreciated that the footprint grid  400  can have more or less than 3 rows/columns and that the disclosed embodiment is not to be limited to any particular array or array size. As will be discussed below in more detail, the footprint grid  400  will be used as a kernel for the disclosed convolution technique. 
         [0032]    The event footprint  300  is then used to determine the ratio/amount of each footprint cell&#39;s FC1, FCm area that is covered by the footprint&#39;s  300  shape. These ratios are referred to herein as the shape coverage factors.  FIG. 5  illustrates an example of shape coverage factors SCF1, . . . , SCFm for the cells FC1, . . . , FCm within the footprint grid  400  illustrated in  FIG. 4 . As noted above, the footprint grid  400  and its shape coverage factors are used as a kernel K in subsequent convolution processing. As can be seen, the first and last footprint cells FC1, FCm (and others) have a shape coverage factor SCF1, SCFm of 0.15 (i.e., only 15% of their respective areas are covered by the footprint  300 ) while the center footprint cell FCc has a shape coverage factor SFCc of 1.0 (i.e., 100% of its area is covered by the footprint  300 ). In one embodiment, the preparation of the footprint grid  400  can be done at runtime (e.g., in a similar manner that grid  200  is created), which allows for the flexibility of selecting shapes from a spatial library without the need to manually process the shape. This also removes the need to store the grid cell coordinates in a database, and also allows for retaining information such as the shape coverage factors SCF1, . . . , SCFm. 
         [0033]    Once the two grids  200 ,  400  are generated, they are formatted in a way to apply convolution processing to complete the risk exposure determination analysis. For example, convolution problems lend themselves nicely to the techniques of discrete Fourier transforms (DFTs). The most common fast convolution algorithms use fast Fourier transform (FFT) algorithms via the circular convolution theorem. That is, the circular convolution of two finite-length sequences is found by taking an FFT of each sequence, multiplying point-wise, and then performing an inverse FFT. An open source project called FFTW (Fastest Fourier Transform in the West—http://fftw.org) is an example of a library of computer applications that can be used for DFT calculations. There are other similar libraries available, a few examples are cufft from NVidia (https://developer.nvidia.com/cufft) and applications in the Intel Math Kernel Library (http://software.intel.com/sites/products/documentation/hpc/mkl/mklman/GUID-BE3BF27D-D852-4C7A-BD38-4409D54E1B1A.htm). 
         [0034]    Since the kernel K (i.e., footprint grid  400  containing the shape coverage factors SCF1, . . . , SCFm) will be applied against the insured location grid  200  via e.g., circular convolution, it is desired that padding should be added to the insured location grid  200  to avoid a “wrap around” effect that could adversely impact the convolution results. This padding is referred to herein as an apron and is a function of the dimensions of the kernel/footprint grid&#39;s  400  shape. 
         [0035]      FIG. 6  illustrates an example data grid  600  having an apron  200   a  comprising kernel padding cells KPC1, . . . , KPCx around the insured location grid  200 .  FIG. 6  also illustrates example anchoring techniques for a kernel (discussed below in more detail). One of skill in the art will appreciate that since the kernel/footprint grid  400  is a 3×3 matrix, the outside cells (e.g., C1, Cn) of the insured location grid  200  need to be padded by two cells. As such, the grid  600  illustrated in  FIG. 6  has an apron comprising two columns to the left of the first column in the insured location grid  200 , two columns to the right of the last column in the insured location grid  200 , two rows above the first row in the insured location grid  200 , and two rows below the last row in the insured location grid  200 . 
         [0036]    Once the data grid  600  is prepared, convolution processing may begin. Specifically, the kernel K (i.e., footprint grid  400  and its shape coverage factors SCF1, . . . , SCFm) is moved across the grid  600  to provide convolution results to each cell in the manner described below. In one embodiment, the bottom left cell in the kernel K is anchored to a cell within the grid  600 . The kernel&#39;s K shape coverage factors SCF1, . . . , SCFm are then multiplied with the summations in the grid  600  cells covered by the kernel (it should be appreciated that the summations for apron cells is 0). All of these values (i.e., products) are then added together and that sum (i.e., the convolution result) is associated with the cell the kernel K is anchored to. For example, in situation (a), the kernel K is anchored at cell  600   a  and multiplied with the summations in the cells within area  602   a , and the products are added to achieve a convolution result for cell  600   a  (shown in  FIG. 7 ). In situation (b), for example, the kernel K is anchored at cell  600   b  and multiplied with the summations in the cells within area  602   b , and the products are added to achieve a convolution result for cell  600   b . As noted above, it is desirable to implement this processing using DFFTs or FFTs with the grid  600  and kernel K as inputs. One of skill in the art would understand how to implement the convolution processing with DFTs or FFTs. The process is performed for each cell in the grid  600  (i.e., each cell is an anchoring point and obtains a convolution result by applying the kernel K to the appropriate cells). 
         [0037]      FIG. 7  illustrates an example grid  700  with convolution results within its cells. As can be seen, the result in cell  600   a  is $340,000 (based on the calculations within area  602   a ) and the result in cell  600   b  is $30,000 (based on the calculations within area  602   b ). From these results, a determination of the highest risk exposure can be made. 
         [0038]    It should be appreciated that the present technology can be applied to more complex insurance policy structures such as those used by commercial insurance policies. The present technology can be adapted to handle more complex shapes that represent catastrophes or other events. It should be appreciated that the present technology may apply to a multitude of shapes (perhaps hundreds or thousands) through the application against the same portfolio of insured locations, if desired. 
         [0039]    From the foregoing, it will be appreciated that although specific examples have been described herein for purposes of illustration, various modifications may be made without deviating from the spirit or scope of this disclosure. It is therefore intended that the foregoing detailed description be regarded as illustrative rather than limiting, and that it be understood that it is the following claims, including all equivalents, that are intended to particularly point out and distinctly claim the claimed subject matter.