Daniele Ritelli

Predation among technologies on the market: A modellistic analysis

The problem of technological predation on the market is analysed using techniques widespread in biomathematics. We first examine the attempt to supplant a technology by introducing an alternative technology, and then consider a market in which a single production technology is available.

Higher Order Approximation of the Period-energy Function for Single Degree of Freedom Hamiltonian Systems

AbstractIn 1985 Franz Rothe [J. Reine Angew Math. 355 (1985) 129–138] found, by means of the thermodynamical equilibrium theory, an asymptotic estimate of the period of solutions of ordinary differential equations originated by predator–prey Volterra–Lotka model. We extend some of the Rothes ideas to more general systems: n

The Goodwin cycle improved with generalized wages: phase portrait, periodic behaviour

dot pleft( t right) = - gleft( {qleft( t right)} right),quad dot qleft( t right) = fleft( {pleft( t right)} right),

Optimal Trading Execution with Nonlinear Market Impact: An Alternative Solution Method

n and succeed in calculating the periods asymptotic analytic expression as a function of the energy level. We finally check our result re-obtaining classical periods estimation of some popular Hamiltonian systems. We apply our technique also to a non-linear Hamiltonian system whose period is not available in the literature.

Elliptic integral solutions of spatial elastica of a thin straight rod bent under concentrated terminal forces

The problem of competitiveness among different technologies is analysed using ordinary differential equations and dynamic systems techniques. Specifically, we have made large use of Lyapunov linearized stability criterion. We have dealt with different kinds of conditions in the market: the static, the dynamic and unbalanced. In all cases we have considered the problem of penetrability of the market at the very beginning of the introduction of a new technology.

The hyperelliptic integrals and π

Abstract The Goodwin cycling of developed economies has been by us modelled in a more general way by representing the Phillips curve f (v) beyond linearity through a growing and convex function of the employment share v . Then, by means of the Lambert functions, we express in exact and explicit form the phase portrait (u, v) of the differential system in the share u(t) of production absorbed by wages, and v(t) itself. Under easy assumptions it is proved that the (u, v) system: is such that all its not-constant solutions shall be periodic. After such a periodicity has been assessed, based on our previous work, an asymptotic (low-energy) expression of the period/energy function is computed, establishing a sufficient condition for its monotonicity.

Relativistic brachistochrones under electric or gravitational uniform fields

Abstract In this paper a costs functional is assumed asymmetrical for the production and the inventory charges: As a state variable, the deviation u(t) = Iid(t)− Ire(t) between the inventories has been chosen. Obviously the manufacturer wishes to keep the cost-functional C(u) as a minimum. The relevant Euler-Lagrange time-equation ü(t) =α2u(t) + 2u(t)3, is faced with the initial condition u(0) = u0 ≠ 0 ; and with the final condition u(T) = 0 meaning that after a time T > 0 the deviation u(t) is re-absorbed at all. In the article the above nonlinear boundary value problem is solved through a much more tractable nonlinear (Cauchy) initial value problem, plus a “shooting”. The integration is carried out by means of the Jacobi elliptic functions, which do here their appearance in a micro-economic context for the first time. After having so detected the “optimal” deviation time law u(t) , a new production plan is then designed for driving the deviation till to its extinction within T .

Actuarial values calculated using the incomplete Gamma function

We consider the optimal trade execution strategies for a large portfolio of single stocks proposed by Almgren (2003). This framework accounts for a nonlinear impact of trades on average market prices. The execution strategy of Almgren (2003) is based on the assumption that no shares per unit of time are trade at the beginning of the period. We use a general solution method that accomodates the case of positive initial trades. Our results are twofold. First of all, we show that the problem admits a solution with no trading in the opening period only if additional parametric restrictions are imposed. Second, with positive initial trading, the optimal execution time depends on trading activity in the initial period.