NON-ROBUSTNESS OF SOME IMPULSE CONTROL PROBLEMS WITH RESPECT TO INTERVENTION COSTS

We study how the value function (minimal cost function) V c of certain impulse control problems depends on the intervention cost c. We consider the case when the cost of interfering with an impulse control of size ζ∈R is given by with c≥0,λ>0 constants, and we show (under some assumptions) that V c is very sensitive (non-robust) to an increase in c near c=0 in the sense that The paper provides a general scheme to prove results of this type. In particular, we show that the scheme applies to several of the standard processes used in financial markets, i.e., Brownian motion, Geometric Brownian motion with jumps, and the Ornstein–Uhlenbeck process.

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