Sequential risk-taking task is defined as engagement in behaviors that simultaneously involve a high potential for punishment and opportunity for reward, and it has become a popular research topic in many fields, such as cognitive psychology, behavioral economics, and social science. This thesis aims to model human behavior in a commonly used measure of risk-taking known as the Balloon Analogue Risk Task (BART) that has been shown to identify individuals who are prone to highly risky behavior. In this laboratory paradigm, participants engage in computer simulation where a balloon is pumped in order to accumulate money, but when the balloon is pumped too high it explodes, and the money that could have been gained is lost. Modeling behaviors in BART is thus to estimate a probability that the Risk-Taking Decision Maker (RTDM) will pump the balloon or stop at each opportunity. In this thesis, I will present a family of learning and evaluation models, which concur in the assumptions: the RTDMs believe that all the balloons in a series are governed by the same stochastic process, and thus experience with past balloons informs subjective probability (SP) for the current one. We discuss three specific learning models in this family as follows,

(i) Stationary model. It postulates that a RTDM assumes that explosion probabilities remain constant with pump opportunities, and the RTDM does not know this probability but has a prior distribution, which is updated optimally with experience.

(ii) Increasing model. It assumes that a RTDM treats the explosion probability as increasing with pump opportunities.

(iii) Prediction Model. Based on the increasing model, this model further uses the result of past balloon as a prediction prior for current decision.

Furthermore, I will introduce an evaluation process of decision option (i.e. puming or stopping) for the three proposed models. Then I will discuss the optimal parameter learning using the principle of maximum likelihood to evaluate the model which fits human behavior the best. At the end, the discussion of connecting BART to real-world risk taking behaviors will be presented briefly, and a series of future work will be summarized.