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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Official URL: http://mor.journal.informs.org/cgi/content/abstrac...

Related URL: http://dx.doi.org/10.1287/moor.17.3.740

## Abstract

Let X(·) be an Ito process with reflection at 0 and state space [0, ∝) and with nonanticipating infinitesimal coefficients μ(·) and σ(·). Let L^{X}(·) 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(L^{X}(T_{a}) ≤y|X(0) = x) over all X in Σ(x) where T_{a} = 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/σ^{2}.

Item Type: | Article |
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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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