We study the Stark effect on excitonic complexes confined in a GaAs-based single quantum well. We approach this problem using Path Integral Monte Carlo methods to compute the many-body density matrix. The developed method is applied for investigation of the electric field-dependence of energies, particle distribution and effective exciton dipole moment. Using these results as an input we apply thermodynamical Monte Carlo methods to investigate systems of several tens to thousands indirect excitons in a 2D quantum well with a lateral confinement arising from the quantum confined Stark effect. Depending on the field strength, exciton density and temperature different phases (gas, liquid and solid) of indirect excitons are predicted.