Scenario optimization

• US 5,148,365 A
• Filed: 08/15/1989
• Issued: 09/15/1992
• Est. Priority Date: 08/15/1989
• Status: Expired due to Term

• Current Assignee: International Business Machines Corporation
• Original Assignee: Ron S. Dembo
• Inventors: Dembo, Ron S.
• Primary Examiner(s): Smith, Jerry
• Assistant Examiner(s): Trammell, Jim
• Application Number:
  US07/394,081
• Time in Patent Office: 1,127 Days
• Field of Search: 364/402, 364/401, 364/408
• US Class Current: 705/36.00R
• CPC Class Codes: G06Q 10/06 Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
• CPC Class Codes: G06Q 40/02 Banking, e.g. interest calculation or account maintenance credit or loans G06Q40/03
• CPC Class Codes: G06Q 40/06 Asset management; Financial planning or analysis

Abstract

A method and apparatus are provided for optimally allocating available resources in a physical system defined by a mathematical model having parameters of uncertain values. The method comprises the steps of firstly assigning a value to each of the uncertain parameters in the mathematical model based on a scenario that may or is expected to occur. Thereafter, given the parameter values at each possible scenario, the mathematical model is solved to yield the best solution of the mathematical model for that scenario. Once this has been complete, a probability value representing the expected probability that the scenario will occur is assigned to each scenario solution. The scenario parameter values, scenario solutions and scenario probabilities are then used to determine a single solution to the mathematical model which best "fits" the desired system behavior under the uncertainty defined by all of the scenarios considered. The single solution is then used to allocate the resources in the system. The present method is particularly useful in modelling a target portfolio from a number of other financial instruments.

Claims

1. A system for allocating available resources in a physical system defined by a mathematical model having at least one parameter of uncertain value to satisfy uncertain levels in a set of demands on said available resources and meet a predetermined set of objectives based on foreseeable future changes of said levels, said system comprising:

resource allocation determining means having input means and memory means, said resource allocation determining means;

i) receiving values for said at least one parameter of uncertain value based on scenarios of said set of demands that may or are expected to occur via said input means;

ii) solving the mathematical model using said values for said at least one parameter for each of said scenarios to yield a best scenario solution of that mathematical model for each scenario;

iii) receiving a probability value for each scenario solution, said probability value representing the likelihood that the scenario will occur;

iv) determining a single solution to the mathematical model which best tracks the desired system behavior under all possible scenarios relative to the probabilities assigned to the scenarios;

output means connected to said resource allocation determining means, said output means providing a physical indication as to how the available resources should be allocated in said physical system based on said single solution to satisfy said set of demands and meet said set of objectives; and

means for adjusting the physical system in accordance with the physical indication.

2. A system as defined in claim 1 wherein said set of objectives are variable, said resource allocation means allowing said set of objectives to be entered therein via said input means and storing said set of objectives in said memory means.

3. A system as defined in claim 2 wherein said resource allocation determining means further places predetermined additional constraints on the mathematical model defining the physical system prior to performing step iv), said constraints being based on operating bounds of the physical system.

4. A system as defined in claim 3 wherein said resource allocation determining means determines said single solution by minimizing a co-ordinating or tracking function.

5. A system as defined in claim 4 wherein said co-ordinating or tracking function further includes an objective term and wherein said resource-allocation-determining-means determines said single solution also by minimizing said objective term.

6. A system as defined in claim 5 wherein said tracking function is of the form ##EQU17## and is minimized by said resource allocation determining means.

7. A system as defined in claim 5 wherein said co-ordinating model is of the form ##EQU18## Where ∥

..∥

denotes any one or two sided norm and is minimized by said resource allocation determining means.

8. A system for replicating a target portfolio of financial instruments using a plurality of second financial instruments, said target portfolio being defined by a mathematical model having at least one parameter of uncertain value, said system comprising:

portfolio generating means having input means, said portfolio generating means;

1) receiving a value for each of the parameters of uncertain value based on a scenario that may or is expected to occur via said input means;

2) solving the model for each scenario to yield the best solution of the model for each scenario;

3) receiving a probability value, representing the likelihood that the scenario will occur, for each solution of the model via the input means;

4) determining a single solution to the mathematical model which best models the behavior of the target portfolio under the uncertainty defined by all of the scenarios considered using the values assigned to the parameters, the solutions of the model and the probabilities assigned to the solutions for all scenarios;

5) selecting appropriate numbers of each of said second financial instruments as determined by said single solution;

output means connected to said portfolio generating means, said output means providing a physical indication as to the selection of said second financial instruments to generate a portfolio of second instruments that best tracks the behavior of said target portfolio based on said single solution; and

means for creating said portfolio of second instruments in accordance with said physical indication.

9. A system as defined in claim 8 wherein the value of said target portfolio is calculated at each scenario.

10. A method of replicating a target option from a plurality of financial instruments including traded options, said target option being represented by a mathematical model having at least one parameter of uncertain value, said method comprising the steps of:

1) selecting a list of financial instruments to be used to replicate the said target option;

2) specifying scenarios by assigning values to the parameters of uncertain value based on scenarios that may or are expected to occur;

3) assigning a probability value to each scenario representing the likelihood that the scenario will occur;

4) calculating the value of the target option for all of the scenarios considered;

5) calculating the value of the selected financial instruments for all scenarios;

6) calculating the optimal composition of financial instruments at each scenario and the cost thereof;

7) calculating the optimal composition of financial instruments under all of the scenarios to yield a portfolio of financial instruments which tracks said target option; and

8) creating a portfolio of financial instruments in accordance with said optimal composition of financial instruments under all scenarios.

11. A method as defined in claim 10 further comprising the step of specifying cost constraints and the optimization method used to perform steps 4 to 8 prior to performing step 4.

12. A method as defined in claim 11 further comprising the step of calculating the value of the optimal composition of the replicating portfolio at each scenario.

13. A method as defined in claim 12 wherein the parameters of uncertain value relate to volatility, interest rates, cost-of-carry and underlying asset prices.

14. A system for replicating a target portfolio of financial instruments from a plurality of second financial instruments, said target portfolio being defined by a mathematical model having at least one parameter of uncertain value, said system comprising:

input means allowing a user to assign values to each of the parameters in each of the scenarios expected to occur and a probability value representing the likelihood that the scenario will occur;

processing means in communication with said input means, said processing means solving the mathematical model for each scenario to yield the best solution of the model for that scenario and determining a single solution to the mathematical model which best tracks the behavior of the target portfolio under all of the scenarios, relative to the probabilities assigned to said scenarios;

memory means for storing a list of second instruments, said processing means selecting appropriate numbers of each of said second instruments as determined by said single solution;

output means connected to said processing means, said output means providing a physical indication as to the selection of said second instruments to generate a portfolio of second instruments that best tracks the behavior of said target portfolio; and

means for creating said portfolio of second instruments in accordance with said physical indication.

15. A method of allocating resources in the optimal management of reservoirs in a hydroelectric system which accounts for the uncertainty in the future demand for the electricity, the uncertainty of water inflow to the reservoirs and the randomness in the functions describing the benefit of using hydroelectricity over thermal generation, said method comprising the steps of:

1) defining a mathematical optimization model that maximizes the benefit of using hydroelectric generation over thermal generation subject to limits on the control of water released through turbines in said hydroelectric system and on water levels in the reservoirs and assuming known water inflow parameters, known electricity demand parameters and known hydro benefit function parameters;

2) defining scenarios for all parameters in said optimization model that are uncertain at future points in time;

3) assigning a value to each uncertain parameter in each of the said scenarios;

4) assigning a probability value to each defined scenario, said probability valve representing the likelihood that the scenario will occur;

5) determining a solution to the optimization model for each scenario using the values assigned to the uncertain parameters for said scenario;

6) determining a single solution to the optimization model which best tracks the desired behaviour of the hydroelectric system under all possible future scenarios, relative to the probabilities assigned to the future scenarios; and

7) setting reservoir levels and hydro releases in said hydroelectric system based on said single solution obtained.

16. A method as defined in claim 15 wherein step (6) is determined by using a tracking function.

17. A method as defined in claim 16 wherein said tracking function is of the form ##EQU19## where c is the current cost of the resource/financial instrument x_j and C is the budget for replication/resource allocation.

18. A method as defined in claim 16 wherein said tracking function is of the form ##EQU20## Where ∥

...∥

denotes any one or two sided norm and where c is the current cost of the resource/financial instrument x_j and C is the budget for replication/resource allocation.