Intertemporal Time Preference on a Simplex in Continuous Time

This work aims to provide a representation theorem for consumption in simplex in continuous time by using a weaker axiom of ’Agree with’, a strong axiom of ’Preferential Independence’,[10, 9], and axioms of ’Separability’ and ’Measurability’ on Simplex provided by Qin and Rommeswinkel in 2022 [20]. Consistently, this work follows the spirit of Koopman’s work between 1960-1972[12, 13, 14], and Epstein’s work in 1983 and 2003[4, 5]. This work considers a model containing discontinuous streams (or trajectories[19]) of outcome in simplex, which is a subset of product space with empty interior. From the main result, the representation of the Expected utility function is naturally derived because it’s a linear case extended by homogeneous