Large-scale particle physics experiments have provided a vast amount of high-quality data during the last decades. A leading role has been played by the Large Hadron Collider where the evaluation and analysis of its second run is currently still in progress while the third run is about to start, promising ever higher precision data of particle collisions and subsequent decays. The agreement between experimental observations and theoretical predictions using the Standard Model of Particle Physics is excellent. Indeed, this is a problem since there are currently few clues for how genuine shortcomings of the model can be overcome. New physics phenomena can appear either at higher energies, which would require the construction of an even larger particle collider, or as small deviations accessible only through precision calculations. These involve higher-order quantum corrections which pose technical challenges. An alternative to the traditional method has been proposed in the form of the loop-tree duality theorem. A derivation of the theorem based on the application of the Cauchy residue theorem is presented and the application of the loop-tree duality to the two loop sunrise amplitude is demonstrated in detail. Further, the appearance of singularities in the dual integrands is analyzed. Cancellations between unphysical singularities are demonstrated. In this work a newly found purely causal representation of the dual integrands and the definitions of several classes of multiloop topologies as well as their loop-tree duality representations are presented. The main part of this work is focused on the development of a framework for using asymptotic expansions in the context of the loop-tree duality. Previously found expansions in the leading order Higgs boson decay are analyzed and their limitations pointed out. A general method is derived for defining asymptotic expansions of scattering amplitudes within the loop-tree duality framework. This method involves the expansion of the dual propagator in a general form that is easily applicable to any given kinematic limit. This expanded propagator is used in the calculation of the scalar two-point function. Upon integration a master expansion is obtained, which can be evaluated for a variety of kinematic limits. Convergence is obtained both at the level of the integrand as well as for the integrated result. The tested limits are: one large mass, a large external momentum, and the threshold limit (both below and above threshold). A separate method for expanding the dual integrand is derived by dividing the integration range into two dual regions such that the integrand can be expanded separately using a Taylor series. This method takes direct advantage of the Euclidean nature of the dual integrand. It has been successful for the scalar two-point function. In the following, the method is applied to the scalar three-point function and tested for two different limits. A multiloop expansion has been achieved for the case of the maximal-loop-topology. Finally, an application to a physical amplitude is shown: the process q q -> H g, which is one of the amplitudes contributing to highly boosted Higgs boson production. Also for this process one limit below and one above threshold were tested successfully.