Reflecting ito processes in a stochastic control problem

Athreya, K. B. ; Weerasinghe, A. (1992) Reflecting ito processes in a stochastic control problem Mathematics of Operations Research, 17 (3). pp. 740-750. ISSN 0364-765X

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Let X(·) be an Ito process with reflection at 0 and state space [0, ∝) and with nonanticipating infinitesimal coefficients μ(·) and σ(·). Let LX(·) be the process of local time at 0 for this X. Suppose that, for each t, (σ(t), μ(t)) are restricted to be in the set A(X(t)) where {A(y); 0 ≤ y < ∞} is a given family of sets in R+ × R. Let Σ(x) be the class of all such Ito processes satisfying X(0) = x. Consider the stochastic control problem of maximizing P(LX(Ta) ≤y|X(0) = x) over all X in Σ(x) where Ta = inf{t :X(t) = a}. It is shown here (under a natural hypothesis on the family A(·)) that for all (a, y) in R+ × R+ and all x in [0, a) the optimal solution is a reflecting diffusion which maximizes μ/σ2.

Item Type:Article
Source:Copyright of this article belongs to Institute for Operations Research and the Management Sciences.
Keywords:Continuous Time Stochastic Control; Reflecting Diffusions; Local Times; Ito Processes
ID Code:1115
Deposited On:05 Oct 2010 12:54
Last Modified:12 May 2011 09:59

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