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
\( \frac{dV_c}{dc}=\infty \ at \ c=0. \)
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 ).
Article PDF
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Accepted 23 April 1998
Rights and permissions
About this article
Cite this article
Øksendal, B. Stochastic Control Problems where Small Intervention Costs Have Big Effects. Appl Math Optim 40, 355–375 (1999). https://doi.org/10.1007/s002459900130
Issue Date:
DOI: https://doi.org/10.1007/s002459900130