1. A portable monitoring device comprising: a hearing aid having a hearing aid housing, at least one microphone for receiving ambient sound, an acoustic signal processor configured to process a signal from the microphone in accordance with a hearing impairment of a person using said hearing aid to obtain a processed sound signal, and an acoustic output transducer configured to produce an acoustic output corresponding to the processed sound signal, and an EEG monitoring system configured to monitor EEG signals of said person, said EEG monitoring system being arranged at least partly in said hearing aid housing, said EEG monitoring system comprising a measuring unit having electrodes for measuring one or more EEG signals from said person, said electrodes being arranged external to the housing or at an outer surface of the housing, a processing unit having an EEG signal processor configured to analyze the EEG signal, said processing unit being arranged in said housing, said EEG signal processor being adapted for, based on the EEG signal, identifying or predicting specific biological incidences, in said person, said processing unit comprising a decision component for deciding, based on said analyzed EEG signal, when an alarm or information must be provided to said person, and a notification component for providing said alarm or information through said output transducer; and an adjustment component receiving a signal representing an acoustic background noise level and configured to adjust a sound level of said alarm or information according to the acoustic background noise level in order to make the alarm or information clearly discernible over background noise.