Alphabetical optimal designs, found by minimising a scalar function of the inverse Fisher information matrix, represent the de-facto standard in optimal design of experiments. For example, the well-known D-optimal design is found by minimising the log determinant of the inverse Fisher information matrix. An alternative decision-theoretic basis for frequentist design is proposed whereby designs are found by minimising the risk function defined as the expectation of an appropriate loss function. The conceptual advantages of the decision-theoretic framework over alphabetical optimal designs will be discussed. However, finding such designs is complicated due to the considerable computational challenges of minimising an analytically intractable risk function, leading to the need for suitable approximation methods. A number of approximation methods are proposed to generate frequentist decision-theoretic optimal designs for different classes of models. Comparison between these approximations will be considered in terms of performance and computing time.