This paper completes the analysis of Choulli et al. Non-Arbitrage up to
Random Horizons and after Honest Times for Semimartingale Models and contains
two principal contributions. The first contribution consists in providing and
analysing many practical examples of market models that admit classical
arbitrages while they preserve the No Unbounded Profit with Bounded Risk (NUPBR
hereafter) under random horizon and when an honest time is incorporated for
particular cases of models. For these markets, we calculate explicitly the
arbitrage opportunities. The second contribution lies in providing simple
proofs for the stability of the No Unbounded Profit with Bounded Risk under
random horizon and after honest time satisfying additional important condition
for particular cases of models
