1. An angular position sensor for assembly on a rotating shaft, said rotating shaft being guided rotationally in a support structure, said angular position sensor comprising:
an annular member with an inner surface adapted for coupling by socketing on said rotating shaft absent a relative rotation between them, and a housing in which a permanent magnet is inserted, the angular position sensor further comprising:
a support provided with:
a through hole through which said rotating shaft and said annular member extend, said through hole having an inner surface opposite and close to the annular member with enough radial allowance to enable the relative rotation and movements thereof in the radial direction within a tolerance range;
a cavity, adjacent to the through hole, housing a sensor device capable of detecting variations in the magnetic field caused by said permanent magnet upon rotating with respect to said support together with the annular member; and
at least one anchoring configuration by which said support is fixedly secured with respect to the rotating shaft.
2. The angular position sensor according to claim 1, wherein said support is formed by first and second bodies attached to one another and provided with respective opposite openings which jointly define said through hole with said inner surface around said annular member and retaining configurations which cooperate with retaining surfaces of the annular member to limit its movements in the axial direction with an axial allowance within a tolerance range.
3. The angular position sensor according to claim 2, wherein between the first body and the annular member there is arranged at least one first elastic gasket andor between the second body and the annular member there is arranged at least one second elastic gasket to seal said radial and axial allowances.
4. The angular position sensor according to claim 3, wherein the annular member has formed therein seats in which there are arranged said first and second gaskets.
5. The angular position sensor according to claim 1, wherein said housing in the annular member has the shape of an elongated groove covering at least one arc in the circumferential direction, said groove being open at least in an end surface of the annular member perpendicular to the rotating shaft to receive inserted therein said permanent magnet, which has a shape complementary to that of said groove and is fixed thereto by interference fit or by adhesive.
6. The angular position sensor according to claim 2, wherein said retaining surfaces of the annular member are formed in at least one rib which extends radially outwards from an outer revolution surface of the annular member.
7. The angular position sensor according to claim 6, wherein said rib covers an arc in the circumferential direction and has end surfaces adapted for interfering with at least one stop formed in at least one of the first and second bodies to limit the rotation of the annular member with respect to the support.
8. The angular position sensor according to claim 1, wherein said sensor device has associated therewith connecting pins.
9. The angular position sensor according to claim 8, wherein said cavity housing the sensor device is an open cavity and said connecting pins are integrated in a connector accessible from the outside.
10. The angular position sensor according to claim 8, wherein said cavity housing the sensor device is a closed cavity, closed by the first and second bodies, and said connecting pins emerge out of the cavity through holes formed in at least one of the first and second bodies.
11. The angular position sensor according to claim 1, wherein said sensor device comprises at least two magneto-sensitive members and a processing circuit delivering a signal which is a function of the absolute position of the permanent magnet integrated in said annular member.
12. The angular position sensor according to claim 1, wherein said annular member is coupled to the rotating shaft by means of an intermediate piece or coupling.
13. The angular position sensor according to claim 2, wherein at least one of said first and second bodies has formed therein hook-ending elastic pins which are locked in corresponding coupling configurations formed in the other one of the first and second bodies for their mutual attachment.
14. The angular position sensor according to claim 2, wherein at least one of said first and second bodies has formed therein through holes opposite corresponding threaded holes formed in the other one of the first and second bodies for the installation therein of screws for the mutual attachment of the first and second bodies.
15. The angular position sensor according to claim 1, wherein said tolerance range is within the maximum relative movements allowable between the sensor device and the permanent magnet housed in the annular member without altering the correct operation of the sensor device.
16. The angular position sensor according to claim 2, wherein said sensor device comprises at least two magneto-sensitive members and a processing circuit delivering a signal which is a function of the absolute position of the permanent magnet integrated in said annular member.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A method, implemented via programmed instructions embodied on a computer-readable medium, for estimating economic risk associated with a group of loans according to a set of values of a first variable associated with the group of loans, wherein the first variable corresponds to a predetermined time period during the pendency of the group of loans, the method comprising:
determining via a processor executing the programmed instructions, a statistical dependency structure between a predetermined first distribution of values of a second variable associated with the group of loans and a predetermined second distribution of values of the second variable associated with the group of loans, wherein the statistical dependency structure is based on a Gaussian copula function;
determining via a processor executing the programmed instructions, the set of values of the first variable using the statistical dependency structure; and
estimating via a processor executing the programmed instructions, the economic risk associated, with the group of loans based on the set of values of the first variable associated with the group of loans.
2. The method of claim 1, wherein each value in the first distribution of the second variable corresponds to a first time point prior to the predetermined time period, and each value in the second distribution of the second variable corresponds to a second time point after the predetermined time period.
3. The method of claim 2, wherein the first and second distributions are based on a number of previously generated statistical data paths representative of projected economic conditions during the pendency of the group of loans, and wherein each data path has a corresponding value of the second variable in the first distribution and in the second distribution.
4. The method of claim 3, wherein determining the statistical dependency structure comprises:
transforming the second variable into a first uniform random variable using the first distribution and a second uniform random variable using the second distribution;
transforming the first and second uniform random variables into corresponding first and second standard normal variables;
determining a correlation parameter between the first standard normal variable and the second standard normal variable; and
determining the Gaussian copula function, wherein the Gaussian copula function is a function of the first and second standard normal variables and the correlation parameter.
5. The method of claim 4, wherein determining the set of values of the first variable using the statistical dependency structure comprises:
determining a conditional standard normal distribution of values of the second standard normal variable for each value of the first standard normal variable using the Gaussian copula function, wherein each conditional standard normal distribution represents the probability that a particular value of the second standard normal variable will be realized given each value of the first standard normal variable; and
using each of the conditional standard normal distributions of the second standard normal variable to determine the set of values of the first variable, wherein each individual value of the first variable corresponds to a particular data path.
6. The method of claim 1, wherein the first variable is a future capital reserve requirement.
7. The method of claim 1, wherein the second variable is a net cash flow.
8. The method of claim 1, wherein the first variable is a guaranty fee.
9. The method of claim 1, wherein the group of loans is a group of mortgage loans.
10. A computer implemented method for determining a set of future capital reserve requirements for a group of mortgage loans using a number of predetermined data paths representative of projected economic conditions during: the pendency of the group of mortgage loans, wherein the set of future capital reserve requirements corresponds to a predetermined time period during the pendency of the group of mortgage loans, the method, implemented via programmed instructions embodied on a computer-readable medium, comprising:
determining via a processor executing the programmed instructions, a statistical dependency structure between first and second distributions of net cash flow values for a group of loans based on a Gaussian copula function, the first distribution comprising individual net cash flow values corresponding to each predetermined data path at a first time prior to the predetermined time period, and the second distribution comprising individual net cash flow values corresponding to each predetermined data path at a second time after the predetermined time period; and
determining via a processor executing the programmed instructions, the set of future capital reserve requirements from the statistical dependency structure.
11. The computer implemented method of claim 10, wherein determining the statistical dependency structure comprises:
transforming the first and second distributions into a first uniform random net cash flow variable and a second uniform random net cash flow variable using the second distribution;
transforming the first and second uniform random net cash flow variables into corresponding first and second standard normal net cash flow variables;
determining a correlation parameter between the first and second standard normal net cash flow variables; and
determining the Gaussian copula function, wherein the Gaussian copula function is a function of the first and second standard normal net cash flow variables and the correlation parameter.
12. The computer implemented method of claim 11, wherein determining the set of future capital reserve requirements from the statistical dependency structure comprises:
determining a conditional standard normal distribution of values of the second standard normal net cash flow variable for each value of the first standard normal net cash flow variable using the Gaussian copula function, wherein each conditional standard normal distribution represents the probability that a particular value of the second standard normal net cash flow variable will be realized given each value of the first standard normal net cash flow variable; and
using each of the conditional standard normal distributions of the second standard normal net cash flow variable to determine the set of future capital reserve requirements, wherein each individual capital reserve requirement corresponds to a particular data path.
13. The computer implemented method of claim 10, further comprising estimating via a processor executing the programmed instructions, economic risk associated with the group of mortgage loans using the set of future capital reserve requirements.
14. A system for determining a set of values of a first variable associated with a group of loans, wherein the set of values of the first variable corresponds to a predetermined time period during the pendency of the group of loans, the system comprising:
memory including a predetermined first distribution of values of a second variable associated with the group of loans and a predetermined second distribution of values of the second variable associated with the group of loans; and
a processor coupled to the memory and operable to execute programmed instructions, wherein the programmed instructions:
(a) determine a statistical dependency structure between the predetermined first distribution of values of the second variable associated with the group of loans and the predetermined second distribution of values of the second variable associated with the group of loans, wherein the statistical dependency structure is based on a Gaussian copula function; and
(b) determine the set of values of the first variable using the statistical dependency structure, whereby economic risk associated with the group of loans may be estimated based on the set of values of the first variable.
15. The system of claim 14, wherein each value in the first distribution of the second variable corresponds to a first time point prior to the predetermined time period, and each value in the second distribution of the second variable corresponds to a second time point after the predetermined time period.
16. The system of claim 15, wherein the first and second distributions are based on a number of previously generated statistical data paths representative of projected economic conditions during the pendency of the group of loans, and wherein each data path has a corresponding value of the second variable in the first distribution and in the second distribution.
17. The system of claim 16, wherein the programmed instructions determine the statistical dependency structure by:
transforming the second variable into a first uniform random variable using the first distribution and a second uniform random variable using the second distribution;
transforming the first and second uniform random variables into corresponding first and second standard normal variables;
determining a correlation parameter between the first standard normal variable and the second standard normal variable; and
determining the Gaussian copula function, wherein the Gaussian copula function is a function of the first and second standard normal variables and the correlation parameter.
18. The system of claim 17, wherein the programmed instructions determine the set of values of the first variable using the statistical dependency structure by:
determining a conditional standard normal distribution of values of the second standard normal variable for each value of the first standard normal variable using the Gaussian copula function, wherein each conditional standard normal distribution represents the probability that a particular value of the second standard normal variable will be realized given each value of the first standard normal variable; and
using each of the conditional standard normal distributions of the second standard normal variable to determine the set of values of the first variable, wherein each individual value of the first variable corresponds to a particular data path.
19. The system of claim 14, wherein the programmed instructions further estimate economic risk associated with the group of loans based on the set of values of the first variable associated with the group of loans.
20. The system of claim 14, wherein the first variable is a future capital reserve requirement.
21. The system of claim 14, wherein the second variable is a net cash flow.
22. The system of claim 14, wherein the first variable is a guaranty fee.
23. The system of claim 14, wherein the group of loans is a group of mortgage loans.