Loss distribution calculation system, loss distribution calculation method and loss distribution calculation-use program

A loss distribution calculation method of a loss distribution calculation system, the method comprising:

• 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.

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:

• 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.