Users often formulate their search queries with immature language without well-developed keywords and complete structures. Such queries fail to express their true information needs and raise ambiguity as fragmental language often yield various interpretations and aspects. This gives search engines a hard time processing and understanding the query, and eventually leads to unsatisfactory retrieval results. An alternative approach to direct answer while facing an ambiguous query is to proactively ask clarifying questions to the user. Recent years have seen many works and shared tasks from both NLP and IR community about identifying the need for asking clarifying question and methodology to generate them. An often neglected fact by these works is that although sometimes the need for clarifying questions is correctly recognized, the clarifying questions these system generate are still off-topic and dissatisfaction provoking to users and may just cause users to leave the conversation. In this work, we propose a risk-aware conversational search agent model to balance the risk of answering user's query and asking clarifying questions. The agent is fully aware that asking clarifying questions can potentially collect more information from user, but it will compare all the choices it has and evaluate the risks. Only after then, it will make decision between answering or asking. To demonstrate that our system is able to retrieve better answers, we conduct experiments on the MSDialog dataset which contains real-world customer service conversations from Microsoft products community. We also purpose a reinforcement learning strategy which allows us to train our model on the original dataset directly and saves us from any further data annotation efforts. Our experiment results show that our risk-aware conversational search agent is able to significantly outperform strong non-risk-aware baselines.