Mathematical Sciences: Applications of Stochastic Control toConsumption/Investment Decisions, Equilibrium Analysis and  Production
{'Code': '03040100', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Michael Steuerwalt', 'PO_EMAI': None, 'PO_PHON': None}
This project consists of research suggested in three sub-areas,            of which the first two are closely linked, while the last is                    slightly disjoint.                                                                   In the first area, the general problem is one where money has              to be continuously invested or consumed so that the net benefit of              the total consumption is a maximum.  The investments can be divided             between a bond, with a fixed rate of return, and several risky                  stocks.  Variations such as borrowing and short selling (investing              negative amounts) are possible.  In some previous work the authors              have made some progress on the case where the various rates of                  return are random rather than fixed.  Also in a recent work, by                 means of measure change argument, they have linked the optimal                  consumption rate in feedback form to the functional inverse of the              derivative of the consumption function.  The authors propose                    extensions in infinite versions of the problem,  situations where               borrowing and short selling are restricted, and cases where a                   bankruptcy payment is involved.                                                      The second area, which is closely related to the first, deals              with a multiplicity of agents all pursuing their individually                   optimal consumption and investment policies.  The goal is to                    investigate the equilibrium situation where net investment, and                 creation of wealth are all zero etc. and show the existence of spot             prices.                                                                              The last area, which is slightly disjoint from the above deals             with the control of production in a manufacturing system producing n            commodities on m machines.  The goal is to minimize holding                     inventory costs and production systems so as to meet specified                  demands, even when machines are liable to failure.  The authors                 propose to investigate the case where the failure rate is                       proportional to machine utilization.  They also suggest an extension            where there is a continuum of machines, but this appears less                   convincing.                                                                          The research of this type is of interest to economic theory and            stock management, while at the same time being in the mainstream of             current research efforts in control seen as part of mathematics.
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[{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}, {'Code': '1454', 'Text': 'SYSTEMS THEORY'}]
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