ON THE CONVEXITY OF VALUE FUNCTIONS FOR A CERTAIN CLASS OF STOCHASTIC DYNAMIC PROGRAMMING PROBLEM

It is a common practice in stochastic dynamic programming problems to assume a priori that the value function is either concave or convex and later verify this assumption after the value function has been identified. It is often a difficult task to establish the concavity or convexity of the value f...

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Vydáno v:Stochastic analysis and applications Ročník 20; číslo 4; s. 783 - 789
Hlavní autoři: Clark, Steven P., Kiessler, Peter C.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia, PA Taylor & Francis Group 28.08.2002
Taylor & Francis
Témata:
Applied sciences
Calculus of variations and optimal control
Exact sciences and technology
Mathematical analysis
Mathematical programming
Mathematics
Operational research and scientific management
Operational research. Management science
Sciences and techniques of general use
Economics
Measurable function
Initial condition
Probability space
Stochastic programming
Brownian motion
Value function
Optimal control
Stochastic control
Convex function
Convexity
Infinite horizon
Dynamic programming
ISSN:0736-2994, 1532-9356
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Popis
Shrnutí:It is a common practice in stochastic dynamic programming problems to assume a priori that the value function is either concave or convex and later verify this assumption after the value function has been identified. It is often a difficult task to establish the concavity or convexity of the value function directly. In this paper, we prove that the value function of a certain type of infinite horizon stochastic dynamic programming problem is convex. This type of value function arises frequently in economic modeling.
ISSN:0736-2994
1532-9356
DOI:10.1081/SAP-120006107