1. Portable device ( 1 ) for assisting the management of a physical exertion provided by a subject, comprising: at least one sensor ( 10 , 11 , 12 ) for a physiological parameter, called exertion parameter, evolving as a function of the physical exertion, said sensor being suitable to provide digital data, called exertion data, that are representative of said exertion parameter, at least one device, called positioning device ( 20 ), that is suitable to determine its own position in a given topographical frame of reference and to provide digital data, called positioning data, that are representative of this position, at least one interface ( 98 , 99 ) for communication with a user, at least one memory ( 4 ) in which data, called input data, are capable of being recorded, comprising at least: positioning data provided by said positioning device, exertion data, data that are representative of an itinerary to be travelled in said topographical frame of reference by said subject in the course of the physical exertion, at least one data-processing unit ( 30 ), designed: to generate data, called forecast data, that are representative of the evolution of at least one exertion parameter over the itinerary remaining to be travelled by the subject, as a function of the input data, from equations and from tables of values recorded in at least one memory of the device, to compare these forecast data with predetermined values recorded in at least one memory of said assistance device, to generate data that are representative of a message, the content of which is a function of the result of the comparison of the forecast data and the predetermined values, to transmit said data that are representative of a message to the interface, with a view to the communication of said message to a user.