Stochastic Control Problems where Small Intervention Costs Have Big Effects |
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Authors: | B Øksendal |
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Institution: | (1) Department of Mathematics, University of Oslo, P. O. Box 1053, Blindern, 0316 Oslo, Norway and Institute of Finance and Management Science, Norwegian School of Economics and Business Administration, Helleveien 30, N-5035 Bergen-Sandviken, Norway, NO |
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Abstract: | We study an impulse control problem where the cost of interfering in a stochastic system with an impulse of size ζ∈
R is given by
c+λ|ζ|,
where c and λ are positive constants. We call λ the proportional cost coefficient and c the intervention cost . We find the value/cost function V
c
for this problem for each c>0 and we show that lim
c→ 0+
V
c
=W , where W is the value function for the corresponding singular stochastic control problem. Our main result is that
This illustrates that the introduction of an intervention cost c>0 , however small, into a system can have a big effect on the value function: the increase in the value function is in no proportion
to the increase in c (from c=0 ).
Accepted 23 April 1998 |
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Keywords: | , Impulse control, Vanishing intervention cost, Quasi-variational inequalities, Singular stochastic control, Nonrobustness,,,,,feature, AMS Classification, 93E20, 60G40, 60J65, 49J40, 35R35, |
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