  We present a derivation of Markovian master equation for the out of
equilibrium quantum dot connected to two superconducting reservoirs, which are
described by the Bogoliubov-de Gennes Hamiltonians and have the chemical
potentials, the temperatures, and the complex order parameters as the relevant
quantities. We consider a specific example in which the quantum dot is
represented by the Anderson impurity model and study the transport properties,
proximity effect and Andreev bound states in equilibrium and far from
equilibrium setups.
