ISSN:
1432-0606
Keywords:
Key words. Impulse control, Vanishing intervention cost, Quasi-variational inequalities, Singular stochastic control, Nonrobustness feature. AMS Classification. 93E20, 60G40, 60J65, 49J40, 35R35.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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 ).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002459900130
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