MINIMIZING OR MAXIMIZING THE EXPECTED TIME TO REACH ZERO.

D. Heath, S. Orey, V. Pestien, W. Sudderth

Research output: Contribution to journalArticle

32 Scopus citations

Abstract

We treat the following control problems: the process X//1(t) with values in the interval ( minus infinity , 0 right bracket (or left bracket , infinity )) is given by the stochastic differential equation dX//1(t) equals mu (t) dt plus sigma (t) dW//t, X//1(0) equals x//1 where the nonanticipative controls mu and sigma are to be chosen so that ( mu (t), sigma (t)) remains in a given set S and the object is to minimize (or maximize) the expected time to reach the origin. The minimization problem had been discussed earlier under various restrictions on the set S. Here an improved verification lemma is established which is used to solve the minimization and maximization problems for any S. An application to a portfolio problem is discussed.

Original languageEnglish (US)
Pages (from-to)195-205
Number of pages11
JournalSIAM Journal on Control and Optimization
Volume25
Issue number1
DOIs
StatePublished - Jan 1 1987
Externally publishedYes

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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