# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Minimizing or maximizing the expected time to reach zero. (English) Zbl 0613.93067
The authors consider stochastic control systems described by the Ito differential equation $dx\left(t\right)=a\left(t\right)·dt+b\left(t\right)·dw\left(t\right)$ with nonanticipative controls a(t) and b(t) to be chosen in an admissible set. Deriving an improved verification lemma of its own interest, they solve the problems of finding optimal controls which minimize or maximize the expected time to reach the zero state. They also discuss an application to a portfolio problem.
Reviewer: A.Kistner
##### MSC:
 93E20 Optimal stochastic control (systems) 60G40 Stopping times; optimal stopping problems; gambling theory 60J60 Diffusion processes 49K45 Optimal stochastic control (optimality conditions) 60J70 Applications of Brownian motions and diffusion theory 91B28 Finance etc. (MSC2000)