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A Method for Computing Double Band Policies for Switching between Two Diffusions

Published online by Cambridge University Press:  27 July 2009

Florin Avram  and
Fikri Karaesmen
Florin Avram
Affiliation:
Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
Fikri Karaesmen
Affiliation:
Department of Mechanical, Industrial and Manufacturing Engineering, Northeastern University, Boston, Massachusetts 02115
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Extract

We develop a method for computing the optimal double band [b, B] policy for switching between two diffusions with continuous rewards and switching costs. The two switch levels [b, B] are obtained as perturbations of the single optimal switching point a of the control problem with no switching costs. More precisely, we find that in the case of average reward problems the optimal switch levels can be obtained by intersecting two curves: (a) the function, γ(a), which represents the long-run average reward if we were to switch between the two diffusions at a and switches were free, and (b) a horizontal line whose height depends on the size of the transaction costs. Our semianalytical approach reduces, for example, the solution of a problem recently posed by Perry and Bar-Lev (1989, in Stochastic Analysis and Applications 7: 103–115) to the solution of one nonlinear equation.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 4 , October 1996 , pp. 569 - 590
Copyright
Copyright © Cambridge University Press 1996

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