Controlled Depletion of a Stochastically Varying Resource Pool

Abstract

A method for controlling resource pool depletion includes, at a first time, determining a first remainder of a depletion interval; on the basis of the first remainder, determining a first depletion rate for urging the pool to reach a selected state at the end of the depletion interval; on the basis of the first depletion rate, partially depleting the pool; and at a second time following the first time, determining a second remainder of the depletion interval; receiving state information indicative of a difference between a state of the pool at the first time and a state of the resource pool at the second time; on the basis of the second remainder and the state information, determining a second depletion rate for urging the pool to reach a selected state at the end of the depletion interval; and on the basis of the second depletion rate, partially depleting the pool.

1 . A computer-readable medium having encoded thereon software for controlling depletion of a resource pool, the software including instructions for causing a data-processing system to:
 at a first time,
 determine a first remainder of a depletion interval; 
 at least in part on the basis of the first remainder, determine a first depletion rate for urging the resource pool to reach a selected state at the end of the depletion interval; 
 on the basis of the first depletion rate, partially deplete the resource pool; 
   at a second time following the first time,
 determine a second remainder of the depletion interval; 
 receive state information indicative of a difference between a state of the resource pool at the first time and a state of the resource pool at the second time; 
 at least in part on the basis of the second remainder and the state information, determine a second depletion rate for urging the resource pool to reach a selected state at the end of the depletion interval; and 
 on the basis of the second depletion rate, partially deplete the resource pool. 
   
     
     
         2 . The computer-readable medium of  claim 1 , wherein the software further comprises instructions for defining the selected state to be a fully-depleted state. 
     
     
         3 . The computer-readable medium of  claim 1 ,
 wherein the software further comprises instructions for causing the data-processing system to select a depletion probability representative of the probability that the resource pool will reach the designated state at the end of the depletion interval, and   wherein the instructions for determining a first depletion rate comprises instructions for causing the data processing system to determine the first depletion rate such that the probability that the resource pool will reach the designated state at the end of the depletion interval is at least equal to the depletion probability.   
     
     
         4 . The computer-readable medium of  claim 1 , wherein the software further comprises instructions for causing a data processing system to urge the resource pool to reach a selected state at the end of the depletion interval by altering the composition of resources within the resource pool. 
     
     
         5 . The computer-readable medium of  claim 1 , wherein the software comprises instructions for causing the data-processing system to receive information indicative of financial instruments that comprise the resource pool. 
     
     
         6 . The computer-readable medium of  claim 5 , wherein the software further comprises instructions for causing the data-processing system to receive status information that includes information indicative of a change in value of the financial instruments that comprise the resource pool. 
     
     
         7 . The computer-readable medium of  claim 5 , wherein the software further comprises instructions for causing the data-processing system to enforce a constraint on receiving a distribution from the resource pool. 
     
     
         8 . A computer-readable medium having encoded thereon software for causing a data-processing system to deplete a resource pool, the software comprising instructions for causing a data-processing system to:
 define a plurality of time periods that collectively comprise a depletion interval;   at the end of each time period,
 detect a change in the resource pool; 
 determine a depletion rate that depends at least in part on the detected change, the depletion rate being selected to urge the resource pool to reach a selected depletion state at the end of the depletion interval; and 
 deplete the resource pool by a depletion amount that depends at least in part on the depletion rate. 
   
     
     
         9 . The computer-readable medium of  claim 8 , wherein the software further comprises instructions for causing the data-processing system to alter the content of the resource pool in response to the detected change, the alteration being selected to urge the resource pool to reach the selected depletion state at the end of the selected depletion interval. 
     
     
         10 . The computer-readable medium of  claim 8 , wherein the instructions for causing the data-processing system to deplete the resource pool comprise instructions for causing the data-processing system to maintain a depletion rate having a selected property. 
     
     
         11 . The computer-readable medium of  claim 10 , wherein the instructions for causing the data processing system to maintain a depletion rate having a selected property comprise instructions for causing the data processing system to maintain a constant depletion rate. 
     
     
         12 . The computer-readable medium of  claim 10 , wherein the instructions for causing the data processing system to maintain a depletion rate having a selected property comprise instructions for causing the data processing system to maintain a depletion rate that results in monotonically increasing depletion amounts as measured by a normalized currency. 
     
     
         13 . The computer-readable medium of  claim 10 , wherein the instructions for causing a data-processing system to detect a change in the resource pool comprise instructions for receiving information indicative of performance of constituent financial instruments of the resource pool. 
     
     
         14 . The computer-readable medium of  claim 8 , wherein the software further comprises instructions for causing a data-processing system to enforce a constraint on the depletion amount. 
     
     
         15 . A method for controlling depletion of a resource pool, the method comprising:
 at a first time,
 determining a first remainder of a depletion interval; 
 at least in part on the basis of the first remainder, determining a first depletion rate for urging the resource pool to reach a selected state at the end of the depletion interval; 
 on the basis of the first depletion rate, partially depleting the resource pool; 
   at a second time following the first time,
 determining a second remainder of the depletion interval; 
 receiving state information indicative of a difference between a state of the resource pool at the first time and a state of the resource pool at the second time; 
 at least in part on the basis of the second remainder and the state information, determining a second depletion rate for urging the resource pool to reach a selected state at the end of the depletion interval; and 
   on the basis of the second depletion rate, partially depleting the resource pool.   
     
     
         16 . A method for depleting a resource pool, the method comprising:
 defining a plurality of time periods that collectively comprise a depletion interval   at the end of each time period,
 detecting a change in the resource pool; 
 determining a depletion rate that depends at least in part on the detected change, the depletion rate being selected to urge the resource pool to reach a selected depletion state at the end of the depletion interval; and 
 depleting the resource pool by a depletion amount that depends at least in part on the depletion rate. 
   
     
     
         17 . A system for controlling depletion of a resource pool, the system comprising:
 a resource pool subject to a stochastic disturbance;
 a depletion controller configured to generate a resource control signal for dynamically controlling constituent contents of the resource pool at least in part on the basis of a specified depletion interval and a specified probability that the resources in the resource pool will reach a selected state at the end of the depletion interval. 
   
     
     
         18 . The system of  claim 17 , further comprising means for generating a feedback signal for providing to the depletion controller, wherein the feedback signal includes information about the resource pool.