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Pricing is a fundamental problem in the banking sector, and is closely related to a number of financial products such as credit scoring or insurance. In the insurance industry an important question arises, namely: how can insurance renewal prices be adjusted? Such an adjustment has two conflicting objectives. On the one hand, insurers are forced to retain existing customers, while on the other hand insurers are also forced to increase revenue. Intuitively, one might assume that revenue increases by offering high renewal prices, however this might also cause many customers to terminate their contracts. Contrarily, low renewal prices help retain most existing customers, but could negatively affect revenue. Therefore, adjusting renewal prices is a non-trivial problem for the insurance industry. In this paper, we propose a novel modelization of the renewal price adjustment problem as a sequential decision problem and, consequently, as a Markov decision process (MDP). In particular, this study analyzes two different strategies to carry out this adjustment. The first is about maximizing revenue analyzing the effect of this maximization on customer retention, while the second is about maximizing revenue subject to the client retention level not falling below a given threshold. The former case is related to MDPs with a single criterion to be optimized. The latter case is related to Constrained MDPs (CMDPs) with two criteria, where the first one is related to optimization, while the second is subject to a constraint. This paper also contributes with the resolution of these models by means of a model-free Reinforcement Learning algorithm. Results have been reported using real data from the insurance division of BBVA, one of the largest Spanish companies in the banking sector.