Pilgrim dark energy with apparent and event horizons in non-flat universe

Pilgrim dark energy is an interesting proposal which is based on the conjecture that phantom-like dark energy with strong enough repulsive force can prevent the formation of a black hole. We investigate this conjecture by assuming the apparent and event horizons in non-flat universe and we develop different cosmological parameters. We construct the corresponding equation of state parameter, which indicates that its present values lie in the phantom era of the universe for different ranges of mu (pilgrim dark energy parameter) as well as xi(2) (interacting parameter). It is interesting to mention here that the pilgrim dark energy with event horizon yields a phantom region for all cases of xi(2) with mu < 0. We also develop the omega(Lambda)-omega(Lambda)' plane and explore the thawing as well as freezing region and Lambda CDM limit for these models. The statefinders plane is also constructed, which shows the correspondence with different models such as quintessence and phantom dark energy, Lambda CDM and Chaplygin gas. Finally, we investigate the validity of the generalized second law of thermodynamics with event horizon in a flat as well as non-flat universe.