Necessity of Transversality Conditions for Infinite Horizon Problems

Conditions implying the vanishing of the Hamiltonian at infinity in optimal control problems

“…Then the following theorem holds: (1)(2)(3)(4), assuming that (a) and (b) are satisfied. Then there exists a pair ( p 0 , p(t)), with p 0 ≥ 0 and ( p 0 , p(t)) = 0 for all t ≥ 0, such that p(t) : [0, ∞) → R n is a continuous solution of the adjoint equationṗ…”

Complex stock price dynamics under Max Weber’s spirit of capitalism hypothesis

“…Though cognizant about the underlying fundamental value, agents might be willing B Marco Airaudo marco.airaudo@drexel.edu 1 School of Economics, LeBow College of Business, Drexel University, Office 1035, Gerri C. LeBow Hall, 3220 Market Street, Philadelphia, PA 19104, USA to pay more for an asset if they expect its price to further increase in the future. As shown by Kamihigashi (1998Kamihigashi ( , 2001Kamihigashi ( , 2015, the baseline infinite-horizon asset pricing model due to Lucas (1978) does not allow for bubbles as they would imply a violation of the representative agent's transversality condition (TVC). To address this issue-in particular the recurrence of booms and crashes in stock price data-various works have augmented Lucas's framework with either some kind of market incompleteness, or alternative forms of learning and bounded rationality in expectation formation.…”

Socially optimal social security and education subsidization in a dynastic model with human capital externalities, fertility and endogenous growth

“…It requires more restrictions as shown in Ekeland and Scheinkman (1986), Kamihigashi (2001), and Sagara (2010), among others. For homogenous functions, the transversality conditions are valid under empirically plausible conditions in our model.…”