Developing marketing strategies for a new product or a new target population is challenging, due to the scarcity of relevant historical data. Building on dynamic Bayesian learning, a sequential information collection optimization assists in creating new data points, within a finite number of learning phases. This procedure identifies effective advertisement design elements as well as customer segments that maximize the expected outcome of the final marketing campaign. In this paper, the marketing campaign performance is modeled by a multiplicative advertising exposure model with Poisson jumps. The intensity of the Poisson process is a function of the marketing campaign features. A forward-looking measurement policy is formulated to maximize the expected improvement in the value of information in each learning phase. Solving this information collection optimization is reduced to a mixed-integer second-order cone programming problem. A computationally efficient approach is proposed that consists in solving a sequence of mixed-integer linear optimization problems. The performance of the optimal learning policy over commonly used benchmark policies is evaluated using examples from the property and casualty insurance industry.