Sponsored search advertisement allows advertisers to target their messages to appropriate customer segments at low costs. While search engines are interested in auction mechanisms that boost their revenues, advertisers seek optimal bidding strategies to increase their net sale revenues for multiple keywords under strict daily budget constraints in an environment where keyword query arrivals, competitor bid amounts, and user purchases are random. We focus on the advertiser’s question and formulate her optimal intraday dynamic multi-keyword bidding problem as a continuous-time stochastic optimization problem. We solve the problem, characterize an optimal policy, and bring a numerical algorithm for implementation. We also illustrate our optimal bidding policy and its benefits over heuristic solutions on numerical examples.