Travelers' responses to the risk and the uncertainty involved in their travel choices have been argued to be a research area that can be better addressed by use of a descriptive approach rather than a normative one. Prospect theory, a descriptive model of decision making under conditions of risk and uncertainty, has recently been incorporated into travel behavior modeling. This paper describes some of the major challenges that modelers face when they apply prospect theory to risky travel behavior contexts. In particular, the options available for determination of the values of crucial parameters for prospect theory travel choice models, such as the reference point and the loss aversion factor, are discussed. Prospect theory has originally been proposed to capture the observed choices between alternatives framed as lotteries and gambles and has fruitfully been applied to some settings in economics. However, because of some of the unique characteristics of travel journeys and the environment of decision making, the application of prospect theory to a travel choice context is not trivial. Modeling challenges because of a lack of consensus reference point values and other difficulties in setting values for other parameters are described, and several methodological approaches that can be used to set the values of parameters for prospect theory are suggested and illustrated.