Bubbles in Assets with Finite Life

A non-local free boundary problem arising in a theory of financial bubbles

“…This financial model is briefly presented in §1c, and a more precise derivation can be found in [1]. The stationary version of this model (i.e.…”

“…The goal of this paper is to study an evolution problem that arises in a model of bubbles that result from volatile differences in beliefs among speculators in a financial market. This financial model is briefly presented in §1c, and a more precise derivation can be found in [1] stationary version of this model (i.e. for infinite horizon) was introduced and solved by Scheinkman & Xiong [2].…”

“…We also list a series of qualitative properties such as monotonicity, convexity, asymptotics and large time behaviour that are related to the economic motivation of the problem. A precise derivation of the model from assumptions on the behaviour of investors, as well as a discussion of the economic significance of these qualitative properties will be provided in our forthcoming work [1]. (ii) Monotonicity and convexity 1 : u t ≥ 0, 0 ≤ u x ≤ α(t), u xx ≥ 0.…”

“…A precise derivation of the model from assumptions on the behaviour of investors, as well as a discussion of the economic significance of these qualitative properties will be provided in our forthcoming work [1]. (ii) Monotonicity and convexity 1 : u t ≥ 0, 0 ≤ u x ≤ α(t), u xx ≥ 0.…”

“…(1.9) Remark 1.4. In the models of equilibrium asset-pricing derived in [2] or [1] starting from assumptions on the the behaviour of investors, the condition ρ ≥ λ is always satisfied. Note that the expression ofā(t) in (1.9) shows that for c 1, the free boundary a(t) cannot be non-increasing in time when ρ < λ.…”