The contingent epiderivative and the calculus of variations on time scales

The calculus of variations on time scales is considered. We propose a new approach to the subject that consists in applying a differentiation tool called the contingent epiderivative. It is shown that the contingent epiderivative applied to the calculus of variations on time scales is very useful: it allows to unify the delta and nabla approaches previously considered in the literature. Generalized versions of the Euler-Lagrange necessary optimality conditions are obtained, both for the basic problem of the calculus of variations and isoperimetric problems. As particular cases one gets the recent delta and nabla results.Comment: Submitted 06/March/2010; revised 12/May/2010; accepted 03/July/2010; for publication in "Optimization---A Journal of Mathematical Programming and Operations Research

Optimal contracts in continuous-time models

We present a unified approach to solving contracting problems with full information in models driven by Brownian motion. We apply the stochastic maximum principle to give necessary and sufficient conditions for contracts that implement the so-called first-best solution. The optimal contract is proportional to the difference between the underlying process controlled by the agent and a stochastic, state-contingent benchmark. Our methodology covers a number of frameworks considered in the existing literature. The main finance applications of this theory are optimal compensation of company executives and of portfolio managers

An induction theorem and nonlinear regularity models

A general nonlinear regularity model for a set-valued mapping $F:X\times R_+\rightrightarrows Y$, where $X$ and $Y$ are metric spaces, is considered using special iteration procedures, going back to Banach, Schauder, Lusternik and Graves. Namely, we revise the induction theorem from Khanh, J. Math. Anal. Appl., 118 (1986) and employ it to obtain basic estimates for studying regularity/openness properties. We also show that it can serve as a substitution of the Ekeland variational principle when establishing other regularity criteria. Then, we apply the induction theorem and the mentioned estimates to establish criteria for both global and local versions of regularity/openness properties for our model and demonstrate how the definitions and criteria translate into the conventional setting of a set-valued mapping $F:X\rightrightarrows Y$.Comment: 28 page

Decentralizing the Stochastic Growth Model

The objective of this paper is to propose a number of alternative decentralized interpretations of representative agent style stochastic growth economies and to explore their implications for the generality of this model construct. Under our first interpretation, firms exist forever and undertake all multiperiod investment decisions while consumer-worker-investors only own financial claims to the firm's output. This contrasts with the more standard decentralization approach where firms exist on a period-by-period basis and consumer-workerinvestors have direct title to the economy's capital stock. Under our second interpretation shareholders hire a manager who undertakes the firm's investment decisions in conformity with his incentive contract. The time series properties of the shareholder-manager economy are seen to replicate those of the analogous representative agent economy if and only if the manager's contract assumes a specific form. This suggests the time series properties of an economy where incentive contracts such as stock option plans are pervasive will differ from those of more standard real business cycle models.stochastic growth model; business cycles; delegated management

Fractional Calculus of Variations for Double Integrals

We consider fractional isoperimetric problems of calculus of variations with double integrals via the recent modified Riemann-Liouville approach. A necessary optimality condition of Euler-Lagrange type, in the form of a multitime fractional PDE, is proved, as well as a sufficient condition and fractional natural boundary conditions.Comment: Submitted 07-Sept-2010; revised 25-Nov-2010; accepted 07-Feb-2011; for publication in Balkan Journal of Geometers and Its Applications (BJGA

Recursive Competitive Equilibrium

In this article we define a Recursive Competitive Equilibrium, provide an example and review the related literature. The article is an entry prepared for The New Palgrave: A Dictionary of Economics, 2nd Edition (Palgrave Macmillan: New York).