In this research a new methodology for optimal customer selection in
cross-selling of financial services products, such as mortgage loans and non
life insurance contracts, is presented. Financial services companies tend to
possess significant databases and a long relationship with each customer. In
this situation the challenge becomes to use the database in general and
specific knowledge of the individual target to estimate the probability of a
cross-sale, the cost of a cross-sale attempt, the average discounted future
profit and the uncertainty of the profit of the entire cross-sale attempt for
that individual. Once reliable estimates for the stochastics of the cross-sale
process have been established, one can optimise the cross-sale profit according
to a variety of criteria including return and risk. In this paper, we first
consider the simple question of optimising the average profit, but we also
consider one version of adjusting for risk when optimising cross-sale profits.
Our extensive case study is taken from non-life insurance, where our sales
probability model is provided to us by the company that also provided us with
the data.