  The aim of this work consists in the study of the optimal investment strategy
for a behavioural investor, whose preference towards risk is described by both
a probability distortion and an S-shaped utility function. Within a
continuous-time financial market framework and assuming that asset prices are
modelled by semimartingales, we derive sufficient and necessary conditions for
the well-posedness of the optimisation problem in the case of piecewise-power
probability distortion and utility functions. Finally, under straightforwardly
verifiable conditions, we further demonstrate the existence of an optimal
strategy.
