Constrained portfolio-consumption strategies with uncertain parameters and borrowing costs

This paper studies the properties of the optimal portfolio-consumption strategies in a {finite horizon} robust utility maximization framework with different borrowing and lending rates. In particular, we allow for constraints on both investment and consumption strategies, and model uncertainty on both drift and volatility. With the help of explicit solutions, we quantify the impacts of uncertain market parameters, portfolio-consumption constraints and borrowing costs on the optimal strategies and their time monotone properties.Comment: 35 pages, 8 tables, 1 figur

Minimax Control of Constrained Parabolic Systems

In this paper we formulate and study a minimax control problem for a class of parabolic systems with controlled Dirichlet boundary conditions and uncertain distributed perturbations under pointwise control and state constraints. We prove an existence theorem for minimax solutions and develop effective penalized procedures to approximate state constraints. Based on a careful variational analysis, we establish convergence results and optimality conditions for approximating problems that allow us to characterize suboptimal solutions to the original minimax problem with hard constraints. Then passing to the limit in approximations, we prove necessary optimality conditions for the minimax problem considered under proper constraint qualification conditions

Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry

We consider a series of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set $\Omega$. The considered problems are well studied for the case when $\Omega$ is a unit disc, but barely studied for arbitrary $\Omega$. We derive extremals to these problems in general case by using machinery of convex trigonometry, which allows us to do this identically and independently on the shape of $\Omega$. The paper describes geodesics in (i) the Finsler problem on the Lobachevsky hyperbolic plane; (ii) left-invariant sub-Finsler problems on all unimodular 3D Lie groups (SU(2), SL(2), SE(2), SH(2)); (iii) the problem of rolling ball on a plane with distance function given by $\Omega$; (iv) a series of "yacht problems" generalizing Euler's elastic problem, Markov-Dubins problem, Reeds-Shepp problem and a new sub-Riemannian problem on SE(2); and (v) the plane dynamic motion problem.Comment: 50 pages, 56 figure

The physical world as a virtual reality: a prima facie case

This paper explores the idea that the universe is a virtual reality created by information processing, and relates this strange idea to the findings of modern physics about the physical world. The virtual reality concept is familiar to us from online worlds, but the world as a virtual reality is usually a subject for science fiction rather than science. Yet logically the world could be an information simulation running on a three-dimensional space-time screen. Indeed, that the essence of the universe is information has advantages, e.g. if matter, charge, energy and movement are aspects of information, the many conservation laws could become a single law of conservation of information. If the universe were a virtual reality, its creation at the big bang would no longer be paradoxical, as every virtual system must be booted up. It is suggested that whether the world is an objective or a virtual reality is a matter for science to resolve, and computer science could help. If one could derive core properties like space, time, light, matter and movement from information processing, such a model could reconcile relativity and quantum theories, with the former being how information processing creates space-time, and the latter how it creates energy and matter

Government Spending Composition in a Simple Model of Schumpeterian Growth

This paper investigates the relevance of government purchasing behavior for innovation-based economic growth. We construct a parsimonious Schumpeterian growth model in which demand from the public sphere can effectively alter the economy's rate of technological change. We incorporate results of various empirical studies arguing that public sector demand acts as incentive for private innovation activities. In contrast to the standard Schumpeterian growth framework, we account for industry heterogeneity in terms of innovation potential. This extension allows to bring government demand policy within the realm of the growth policy debate. By varying the composition of its purchases, the government can induce a reallocation of private resources to stimulate the rate of technological change. This comes along with temporarily faster economic growth. Moreover, our welfare analysis implies that it is always worth implementing a policy in which industries benefit from public purchases subject to their specific innovation size.public demand, endogenous technological change, Schumpeterian growth

Inflation and String Cosmology

After 25 years of its existence, inflationary theory gradually becomes the standard cosmological paradigm. However, we still do not know which of the many versions of inflationary cosmology will be favored by the future observational data. Moreover, it may be quite nontrivial to obtain a natural realization of inflationary theory in the context of the ever changing theory of all fundamental interactions. In this paper I will describe the history and the present status of inflationary cosmology, including recent attempts to implement inflation in the context of string theory.Comment: 40 pages, 9 figures, an extended version of my talks at the SLAC Summer School "Nature's Greatest Puzzles," at the conference Cosmo04 in Toronto, at the VI Mexican School on Gravitation, and at the XXII Texas Symposium on Relativistic Astrophysics in 200

An optimal inventory pricing and ordering strategy subject to demand dependent on stock level and price

This article considers the deterministic singular optimal control problem of profit maximisation for inventory replenished at a variable rate and depleted by demand which is assumed to vary with price and stock availability. Optimal policies for the product order rate and price are derived using the maximum principle. Several initial inventory regions are identified as potential inventory states for feasible profit optimisation. Bounds on the maximum price for maximising net profit or minimising loss are obtained. Numerical simulations accompanied by phase diagrams are performed to support the theoretical findings