A mean-field model of optimal investment
arxiv(2024)
摘要
We establish the existence and uniqueness of the equilibrium for a stochastic
mean-field game of optimal investment. The analysis covers both finite and
infinite time horizons, and the mean-field interaction of the representative
company with a mass of identical and indistinguishable firms is modeled through
the time-dependent price at which the produced good is sold. At equilibrium,
this price is given in terms of a nonlinear function of the expected (optimally
controlled) production capacity of the representative company at each time. The
proof of the existence and uniqueness of the mean-field equilibrium relies on a
priori estimates and the study of nonlinear integral equations, but employs
different techniques for the finite and infinite horizon cases. Additionally,
we investigate the deterministic counterpart of the mean-field game under
study.
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