This paper introduces the probabilistic formulation of continuous-time economic models: forward stochastic differential equations (SDE) govern the dynamics of backward-looking variables, and backward SDEs capture that of forward-looking variables. Deep learning streamlines the search for the...

This paper introduces the probabilistic formulation of continuous-time economic models: forward stochastic differential equations (SDE) govern the dynamics of backward-looking variables, and backward SDEs capture that of forward-looking variables. Deep learning streamlines the search for the...

We investigate the entry timing and location decisions under market-size uncertainty with Brownian motions in a continuous-time spatial competition duopoly model a la d'Aspremont et al. (1979). Under a sequential equilibrium, the threshold of the follower non-monotonically increases in...

We study the entry timing and location decisions of two exclusive buyer-supplier relationships in a continuous-time spatial competition model. In each relationship, the firms determine their entry timing and location, and negotiate a wholesale price through Nash bargaining. Then, the downstream...

We study the entry timing and location decisions of two exclusive buyer-supplier relationships in a continuous-time spatial competition model. In each relationship, the firms determine their entry timing and location, and negotiate a wholesale price through Nash bargaining. Then, the downstream...

We investigate the entry timing and location decisions under market-size uncertainty with Brownian motions in a continuous-time spatial competition duopoly model a la d'Aspremont et al. (1979). Under a sequential equilibrium, the threshold of the follower non-monotonically increases in...