  Cai, Song and Kou (2015) [Cai, N., Y. Song, S. Kou (2015) A general framework
for pricing Asian options under Markov processes. Oper. Res. 63(3): 540-554]
made a breakthrough by proposing a general framework for pricing both
discretely and continuously monitored Asian options under one-dimensional
Markov processes. In this note, under the setting of continuous-time Markov
chain (CTMC), we explicitly carry out the inverse Z-transform and the inverse
Laplace transform respectively for the discretely and the continuously
monitored cases. The resulting explicit single Laplace transforms improve their
Theorem 2, p.543, and numerical studies demonstrate the gain in efficiency.
