  When faced with a new customer, many factors contribute to an insurance
firm's decision of what offer to make to that customer. In addition to the
expected cost of providing the insurance, the firm must consider the other
offers likely to be made to the customer, and how sensitive the customer is to
differences in price. Moreover, firms often target a specific portfolio of
customers that could depend on, e.g., age, location, and occupation. Given such
a target portfolio, firms may choose to modulate an individual customer's offer
based on whether the firm desires the customer within their portfolio. We term
the problem of modulating offers to achieve a desired target portfolio the
portfolio pursuit problem. Having formulated the portfolio pursuit problem as a
sequential decision making problem, we devise a novel reinforcement learning
algorithm for its solution. We test our method on a complex synthetic market
environment, and demonstrate that it outperforms a baseline method which mimics
current industry approaches to portfolio pursuit.
