Multi-agent production equilibrium models with expansion

This thesis is concerned with a multi-agent equilibrium expansion model where agents are faced with an exogenous stochastic constant elasticity demand function. Producers simultaneously decide their production schedule, via a sequential equilibrium market clearing condition, as well as their optimal expansion schedule which is formulated as the solution of a singular stochastic control problem. In particular, agents take into account both the fact that their expansion has an adverse effect to the price and also the effect of their actions on the rest of the agents. For every agent, the value function and the optimal control process is determined and a Nash equilibrium for the market is established. The problem is divided into two sections, the monopolist case, where a single agent dominates the market and the competitive case in which all agents form a price-taking continuum, and the problem takes the form of a mean-field stochastic differential game. In both cases the value function as well as the control is calculated in closed form. In a different topic using an implicit numerical scheme and under mild conditions we recover, in a compact way, the optimal weak convergence rate for a Cox–Ingersoll–Ross (CIR) process despite the fact that the coefficients of the underlying Stochastic differential equation are not Lipschitz.