1. A portable electronic device comprising: a battery; a current measurement unit which is connected to the battery and measures a current, the current being output from the battery and flowing through an output current monitoring resistor; a control unit which can execute a plurality of application programs; and a storage unit which stores a current threshold value set for each of the plurality of application programs executable by the control unit, wherein the control unit monitors a current value measured by the current measurement unit and a type of application program being executed, and executes a reset process or a power-off process when the current value measured by the current measurement unit exceeds a current threshold value corresponding to the type of application program currently being executed.