Loss distribution calculation system, loss distribution calculation method and loss distribution calculation-use program
First Claim
1. A loss distribution calculation system, comprising:
- a frequency distribution/scale distribution input section configured to input information about a frequency distribution and a scale distribution;
a scale distribution discretization section configured to perform either one or both of upside and downside discretizations for the input scale distribution;
a sub-composite distribution calculation section configured to calculate, after performing division of all events, a probability value of a cumulative sum of losses for a portion out of all the events in order to calculate either one or both of an upside sub-composite distribution and a downside sub-composite distribution, said upside sub-composite distribution being calculated based on the frequency distribution and the upside-discretized scale distribution, and said downside sub-composite distribution being calculated based on the frequency distribution and the downside-discretized scale distribution;
an accuracy calculation section configured to calculate;
upper and lower bounds of a loss distribution function based on either one or both of the upside and downside sub-composite distributions,a function, as an approximate value of the loss distribution function, based on either one or both of the upside and downside sub-composite distributions, andan accuracy of the approximate value; and
a loss distribution output section configured to output information about the approximate value of the loss distribution function, with guaranteed accuracy, represented by information about the calculated accuracy,wherein;
each of the frequency distribution/scale distribution input section, the scale distribution discretization section, the sub-composite distribution calculation section, the accuracy calculation section, and the loss distribution output section is implemented using hardware;
the upside sub-composite distribution is the total sum of products of a first probability function and a first distribution function, with respect to a subset of instances of a probability variable indicating the number of loss events;
the first probability function is a probability function of a cumulative distribution function of the frequency distribution;
the first distribution function is a distribution function regarding the sum of plural discrete random variables dependent on the upside-discretized scale distribution; and
the downside sub-composite distribution is the total sum of products of a second probability function and a second distribution function, with respect to a subset of instances of a probability variable indicating the number of loss events;
the second probability function is a probability function of a cumulative distribution function of the frequency distribution; and
the second distribution function is a distribution function regarding the sum of plural discrete random variables dependent on the downside-discretized scale distribution.
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Abstract
A loss distribution calculation system including: a section that performs at least one of upside and downside discretizations for a scale distribution; a section that calculates, after dividing all events, a probability value of a cumulative sum of losses for a portion out of all events in order to calculate at least one of upside and downside sub-composite distributions, the upside sub-composite distribution being calculated based on the frequency distribution and the upside-discretized scale distribution, and the downside sub-composite distribution being calculated based on the frequency distribution and the downside-discretized scale distribution; a section that calculates upper and lower bounds of a loss distribution function based on at least one of the upside and downside sub-composite distributions, calculates a function, as an approximate value of the loss distribution function, based on at least one of the upside and downside sub-composite distributions, and calculates an accuracy of the approximate value.
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Citations
8 Claims
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1. A loss distribution calculation system, comprising:
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a frequency distribution/scale distribution input section configured to input information about a frequency distribution and a scale distribution; a scale distribution discretization section configured to perform either one or both of upside and downside discretizations for the input scale distribution; a sub-composite distribution calculation section configured to calculate, after performing division of all events, a probability value of a cumulative sum of losses for a portion out of all the events in order to calculate either one or both of an upside sub-composite distribution and a downside sub-composite distribution, said upside sub-composite distribution being calculated based on the frequency distribution and the upside-discretized scale distribution, and said downside sub-composite distribution being calculated based on the frequency distribution and the downside-discretized scale distribution; an accuracy calculation section configured to calculate; upper and lower bounds of a loss distribution function based on either one or both of the upside and downside sub-composite distributions, a function, as an approximate value of the loss distribution function, based on either one or both of the upside and downside sub-composite distributions, and an accuracy of the approximate value; and a loss distribution output section configured to output information about the approximate value of the loss distribution function, with guaranteed accuracy, represented by information about the calculated accuracy, wherein; each of the frequency distribution/scale distribution input section, the scale distribution discretization section, the sub-composite distribution calculation section, the accuracy calculation section, and the loss distribution output section is implemented using hardware; the upside sub-composite distribution is the total sum of products of a first probability function and a first distribution function, with respect to a subset of instances of a probability variable indicating the number of loss events; the first probability function is a probability function of a cumulative distribution function of the frequency distribution; the first distribution function is a distribution function regarding the sum of plural discrete random variables dependent on the upside-discretized scale distribution; and the downside sub-composite distribution is the total sum of products of a second probability function and a second distribution function, with respect to a subset of instances of a probability variable indicating the number of loss events; the second probability function is a probability function of a cumulative distribution function of the frequency distribution; and the second distribution function is a distribution function regarding the sum of plural discrete random variables dependent on the downside-discretized scale distribution. - View Dependent Claims (2, 3, 4)
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5. A loss distribution calculation method of a loss distribution calculation system, the method comprising:
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inputting, by a processor, information about a frequency distribution and a scale distribution; performing, by the processor, either one or both of upside and downside discretizations for the input scale distribution; calculating, by the processor, after performing division of all events, a probability value of a cumulative sum of losses for a portion out of all events in order to calculate either one or both of an upside sub-composite distribution and a downside sub-composite distribution, said upside sub-composite distribution being calculated based on the frequency distribution and the upside-discretized scale distribution, and said downside sub-composite distribution being calculated based on the frequency distribution and the downside-discretized scale distribution; calculating, by the processor, upper and lower bounds of a loss distribution function based on either one or both of the upside and downside sub-composite distributions, calculates a function, as an approximate value of the loss distribution function, based on either one or both of the upside and downside sub-composite distributions, and calculates an accuracy of the approximate value; and outputting, by the processor, information about the approximate value of the loss distribution function with guaranteed accuracy, represented by information about the calculated accuracy; the upside sub-composite distribution is the total sum of products of a first probability function and a first distribution function, with respect to a subset of instances of a probability variable indicating the number of loss events; the first probability function is a probability function of a cumulative distribution function of the frequency distribution; the first distribution function is a distribution function regarding the sum of plural discrete random variables dependent on the upside-discretized scale distribution; and the downside sub-composite distribution is the total sum of products of a second probability function and a second distribution function, with respect to a subset of instances of a probability variable indicating the number of loss events; the second probability function is a probability function of a cumulative distribution function of the frequency distribution; and the second distribution function is a distribution function regarding the sum of plural discrete random variables dependent on the downside-discretized scale distribution. - View Dependent Claims (6)
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7. A non-transitory computer-readable medium, on which a program is recorded, said program causes a computer to perform a loss distribution calculation method comprising:
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inputting information about a frequency distribution and a scale distribution; performing either one or both of upside and downside discretizations for the input scale distribution; calculating, after performing division of all events, a probability value of a cumulative sum of losses for a portion out of all events in order to calculate either one or both of an upside sub-composite distribution and a downside sub-composite distribution, said upside sub-composite distribution being calculated based on the frequency distribution and the upside-discretized scale distribution, and said downside sub-composite distribution being calculated based on the frequency distribution and the downside-discretized scale distribution; calculating upper and lower bounds of a loss distribution function based on either one or both of the upside and downside sub-composite distributions, calculates a function, as an approximate value of the loss distribution function, based on either one or both of the upside and downside sub-composite distributions, and calculates an accuracy of the approximate value; and outputting information about the approximate value of the loss distribution function with guaranteed accuracy represented by information about the calculated accuracy; wherein; the upside sub-composite distribution is the total sum of products of a first probability function and a first distribution function, with respect to a subset of instances of a probability variable indicating the number of loss events; the first probability function is a probability function of a cumulative distribution function of the frequency distribution; the first distribution function is a distribution function regarding the sum of plural discrete random variables dependent on the upside-discretized scale distribution; and the downside sub-composite distribution is the total sum of products of a second probability function and a second distribution function, with respect to a subset of instances of a probability variable indicating the number of loss events; the second probability function is a probability function of a cumulative distribution function of the frequency distribution; and the second distribution function is a distribution function regarding the sum of plural discrete random variables dependent on the downside-discretized scale distribution. - View Dependent Claims (8)
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Specification