In a discrete-time financial market setting, the paper relates various concepts introduced for dynamic portfolios (both in discrete and in continuous time). These concepts are: value preserving portfolios, numeraire portfolios, interest oriented portfolios, and growth optimal portfolios. It will turn out that these concepts are all associated with a unique martingale measure which agrees with t...

Stochastic optimal growth involves the study of the optimal intertemporal allocation of capital and consumption in an economy where production is subject to random disturbances. The theory traces its roots to the seminal work on deterministic optimal growth by Ramsey [106], Cass [21] and Koopmans [55]. Its influence has been enhanced by research that shows how the convex stochastic growth model...

This paper considers a neoclassical optimal growth problem where the shock that perturbs the economy in each time period is potentially unbounded on the state space. Sufficient conditions for existence, uniqueness and stability of equilibria are derived in terms of the primitives of the model using recent techniques from the field of perturbed dynamical systems. Journal of Economic Literature C...

We provide sufficient conditions on the objective functional and the constraint functions under which the Lagrangean can be represented by a ` sequence of multipliers in infinite horizon discrete time optimal growth models.

The regular nutritional intake of an expectant mother clearly affects the weight development of the fetus. Assuming the growth of the fetus follows a deterministic growth law, like a logistic equation, albeit dependent on the nutritional intake, the ideal solution is usually determined by the birth-weight being pre-assigned, for example, as a percentage of the mother's average weight. This prob...

This paper provides an analysis of weak, Pontryagin and bounded strong minima satisfying a quadratic growth condition for optimal control problems of ordinary differential equations with constraints on initial-final state and pointwise constraints of two types: (a) inequality and equality mixed (control-state) constraints satisfying the hypothesis of uniform linear independence of gradients wit...

The cylindrical lock-release laboratory experiments of Sutherland & Nault (J. Fluid Mech., vol. 586, 2007, pp. 109–118) showed that a radially advancing symmetric intrusive gravity current spreads not as an expanding annulus (as is the case for bottom-propagating gravity currents), but rather predominantly along azimuthally periodic radial ‘spokes’. Here, we investigate whether the spokes are a...

We explore the combined effects of a climate threshold (a potential ocean thermohaline circulation collapse), parameter uncertainty, and learning in an optimal economic growth model. Our analysis shows that significantly reducing carbon dioxide ðCO2Þ emissions may be justified to avoid or delay even small (and arguably realistic) damages from an uncertain and irreversible climate change—even wh...

We analyse the interaction between dividend policy and investment decision in a growth opportunity of a liquidity constrained firm. This leads us to study a mixed singular control/optimal stopping problem for a diffusion that we solve quasi-explicitly establishing connections with two auxiliary optimal stopping problems. We characterize situations where it is optimal to postpone dividend distri...

In this work we ask how should an investor distribute wealth over various assets to maximizethe growth rate of the cumulative wealth in a discrete time market with proportional transactioncosts. We show that this sequential decision problem has a stationary optimal policy. Inaddition, we show that for all 2 > 0 there exists a policy that guarantees a growth rate at most 2bel...