Recent criticisms of the principles and procedures by which insurance premiums have been determined are reviewed. Examples are developed which illustrate the application of the methods of decision analysis to the determination of insurance premiums. Problems such as the measurement of consumer demand for insurance and the quantification of management objectives, which tend to remain in the background in conventional approaches to insurance premiums, must be squarely faced in applying decision analysis. Examples of how Bayesian decision methods may be used to modify initial insurance prices as experience unfolds and to arrive at rational decisions concerning ancillary benefits and options in insurance policies, are presented. The definition of the actuarial function that appears in the organizational chart of most insurance corporations, the dictionary definition of actuarial science, and the description in a university catalogue of a course in actuarial science will usually agree that actuarial science is concerned with the determination of the price of insurance protection. Traditionally one of the primary thrusts in actuarial education has been directed toward teaching students the mathematical techniques through which the present expected value of future insurance benefits, which may be uncertain in amount and occur at uncertain times, and the present ex