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We consider an optimal switching problem where the terminal reward depends onthe entire control trajectory. We show existence of an optimal control byapplying a probabilistic technique based on the concept of Snell envelopes. Wethen apply this result to solve an impulse control problem for stochastic delaydifferential equations driven by a Brownian motion and an independent compoundPoisson process. Furthermore, we show that the studied problem arises naturallywhen maximizing the revenue from operation of a group of hydro-power plantswith hydrological coupling.

A Finite Horizon Optimal Switching Problem with Memory and Application to Controlled SDDEs