  This contribution is concerned with price optimisation of the new business
for a non-life product. Due to high competition in the insurance market,
non-life insurers are interested in increasing their conversion rates on new
business based on some profit level. In this respect, we consider the
competition in the market to model the probability of accepting an offer for a
specific customer. We study two optimisation problems relevant for the insurer
and present some algorithmic solutions for both continuous and discrete case.
Finally, we provide some applications to a motor insurance dataset.
