Stochastic Dynamic Programming in a Computer Using a Multi-Part Utility Function and Local Search to Efficiently Compute Asset Allocation and Consumption
First Claim
1. A method in a computer including processor(s) coupled to a memory, comprising:
- inputting data representing consumption level(s) into the memory, wherein a value of the consumption level(s) represents required consumption C1;
inputting data representing returns of each asset class into the memory;
performing one or more step(s) of stochastic dynamic programming (SDP) in the processor(s) using the data representing the returns of each asset class and values of a utility function U based on the consumption levels to compute values of aggregate utility of wealth, wherein the SDP step(s) includes the following sub-steps;
reading data representing an aggregate utility of wealth Ut+1 for wealth levels Wt+1,1 through Wt+1,M, and a description of single time period utility U;
computing local searches in the processor(s) an optimal asset allocation vector At, an optimal consumption Ct, and an optimal aggregate utility of wealth Ut for a wealth level Wt,1;
computing local searches in the processor(s) the optimal asset allocation vector At, the optimal consumption Ct, and the optimal aggregate utility of wealth Ut for a wealth level Wt,2;
computing local searches in the processor(s) the optimal asset allocation vector At, the optimal consumption Ct, and the optimal aggregate utility of wealth Ut for additional wealth levels up to at least wealth level Wt,M;
storing the values of the aggregate utility of wealth Ut for wealth levels Wt,1 through Wt,M in the memory; and
outputting the optimal asset allocation vector AB and the optimal consumption CB at an initial age B and wealth WB.
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Abstract
The invention relates, among other things, to methods and non-transitory computer-readable medium that include inputting data representing consumption levels into the memory, wherein a value of the consumption levels represents required consumption C1, inputting data representing returns of each asset class into the memory, performing stochastic dynamic programming in the processors using the data representing the returns of each asset class and values of a utility function U based on the consumption levels to compute values of aggregate utility of wealth, storing the values of the aggregate utility of wealth in the memory, computing local searches in the processors of the values of aggregate utility of wealth over an asset allocation and consumption space to compute optimal asset allocation and optimal consumption, storing the optimal asset allocation and optimal consumption in the memory, and outputting the optimal asset allocation and the optimal consumption value for an initial age and wealth.
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Citations
21 Claims
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1. A method in a computer including processor(s) coupled to a memory, comprising:
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inputting data representing consumption level(s) into the memory, wherein a value of the consumption level(s) represents required consumption C1; inputting data representing returns of each asset class into the memory; performing one or more step(s) of stochastic dynamic programming (SDP) in the processor(s) using the data representing the returns of each asset class and values of a utility function U based on the consumption levels to compute values of aggregate utility of wealth, wherein the SDP step(s) includes the following sub-steps; reading data representing an aggregate utility of wealth Ut+1 for wealth levels Wt+1,1 through Wt+1,M, and a description of single time period utility U; computing local searches in the processor(s) an optimal asset allocation vector At, an optimal consumption Ct, and an optimal aggregate utility of wealth Ut for a wealth level Wt,1; computing local searches in the processor(s) the optimal asset allocation vector At, the optimal consumption Ct, and the optimal aggregate utility of wealth Ut for a wealth level Wt,2; computing local searches in the processor(s) the optimal asset allocation vector At, the optimal consumption Ct, and the optimal aggregate utility of wealth Ut for additional wealth levels up to at least wealth level Wt,M; storing the values of the aggregate utility of wealth Ut for wealth levels Wt,1 through Wt,M in the memory; and outputting the optimal asset allocation vector AB and the optimal consumption CB at an initial age B and wealth WB. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
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16. A non-transitory computer-readable medium storing program instructions that cause a computer to perform the following steps, comprising:
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inputting data representing consumption level(s) into the memory, wherein a value of the consumption level(s) represents required consumption C1; inputting data representing returns of each asset class into the memory; performing one or more step(s) of stochastic dynamic programming in the processor(s) using the data representing the returns of each asset class and values of a utility function U based on the consumption levels to compute values of aggregate utility of wealth; storing the values of the aggregate utility of wealth in the memory; computing local searches in the processor(s) of the values of aggregate utility of wealth over an asset allocation and consumption space to compute optimal asset allocation and optimal consumption; and outputting the optimal asset allocation and the optimal consumption value for an initial age and wealth. - View Dependent Claims (17, 18, 19, 20, 21)
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Specification