High-utility itemset mining (HUIM) is one of the heavily studied fields of data mining, which is due to its high compatibility with real-world applications. HUIM is a process of extracting a complete set of interesting patterns by considering the importance and the quantity of each item. Incremental high-utility itemset mining (IHUIM) further increases the compatibility of HUIM by mining from a data stream instead of a static database. It does this by mining interesting patterns in a single database scan and storing prior knowledge in a compact data structure. However, there is a critical limitation, because the importance of each item has to be guaranteed to remain unchanged throughout the data stream. This limitation hinders the compatibility of IHUIM to the real-world applications, because the importance of an item changes from time to time in the real world. Conventional IHUIM approaches consequently have to use outdated information when mining interesting patterns. This paper proposes a novel problem of mining high-utility itemsets in an incremental and dynamic profit environment in order to account for the fluctuation of the item's importance. Furthermore, a novel approach to mining patterns in this type of environment is introduced using an efficient list structure and tight upper bounds. Experiments on real and synthetic datasets show that the proposed approach performs well compared to the state-of-the-art approaches in terms of the runtime and memory usage, and it scales better than the other approaches.