The Experts below are selected from a list of 309 Experts worldwide ranked by ideXlab platform
Luigi Montrucchio - One of the best experts on this subject based on the ideXlab platform.
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Cass Transversality Condition and sequential asset bubbles
Economic Theory, 2004Co-Authors: Luigi MontrucchioAbstract:The objective of this paper is to illustrate the connection existing between the asymptotic value of a certain random series and the absence of asset pricing valuation bubbles in stochastic economies with sequential markets. This series, in turn, is closely related to the one proposed by Cass to characterize efficient accumulation paths in Solow models. Copyright Springer-Verlag Berlin/Heidelberg 2004Bubbles, Transversality Conditions, Sequential asset markets.,
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cass Transversality Condition and sequential asset bubbles
Economic Theory, 2004Co-Authors: Luigi MontrucchioAbstract:The objective of this paper is to illustrate the connection existing between the asymptotic value of a certain random series and the absence of asset pricing valuation bubbles in stochastic economies with sequential markets. This series, in turn, is closely related to the one proposed by Cass to characterize efficient accumulation paths in Solow models.
Mariusz Urbański - One of the best experts on this subject based on the ideXlab platform.
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Random countable alphabet conformal iterated function systems satisfying the Transversality Condition
Nonlinearity, 2016Co-Authors: Mariusz UrbańskiAbstract:Dealing with with countable (finite and infinite alike) alphabet random conformal iterated function systems with overlaps, we formulate appropriate Transversality Conditions and then prove the relevant, in such a context, the Moran–Bowen formula which determines the Hausdorff dimension of random limit sets in dynamical terms. We also provide large classes of examples of such random systems satisfying the Transversality Condition.
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Transversality FAMILY OF EXPANDING RATIONAL SEMIGROUPS
Advances in Mathematics, 2013Co-Authors: Hiroki Sumi, Mariusz UrbańskiAbstract:Abstract We study finitely generated expanding semigroups of rational maps with overlaps on the Riemann sphere. We show that if a d -parameter family of such semigroups satisfies the Transversality Condition, then for almost every parameter value the Hausdorff dimension of the Julia set is the minimum of 2 and the zero of the pressure function. Moreover, the Hausdorff dimension of the exceptional set of parameters is estimated. We also show that if the zero of the pressure function is greater than 2 , then typically the 2-dimensional Lebesgue measure of the Julia set is positive. Some sufficient Conditions for a family to satisfy the Transversality Conditions are given. We give non-trivial examples of families of semigroups of non-linear polynomials with the Transversality Condition for which the Hausdorff dimension of the Julia set is typically equal to the zero of the pressure function and is less than 2 . We also show that a family of small perturbations of the Sierpinski gasket system satisfies that for a typical parameter value, the Hausdorff dimension of the Julia set (limit set) is equal to the zero of the pressure function, which is equal to the similarity dimension. Combining the arguments on the Transversality Condition, thermodynamical formalisms and potential theory, we show that for each a ∈ C with | a | ≠ 0 , 1 , the family of small perturbations of the semigroup generated by { z 2 , a z 2 } satisfies that for a typical parameter value, the 2-dimensional Lebesgue measure of the Julia set is positive.
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Transversality Family of Expanding Rational Semigroups
arXiv: Dynamical Systems, 2011Co-Authors: Hiroki Sumi, Mariusz UrbańskiAbstract:This paper deals with both complex dynamical systems and conformal iterated function systems. We study finitely generated expanding semigroups of rational maps with overlaps on the Riemann sphere. We show that if a $d$-parameter family of such semigroups satisfies the Transversality Condition, then for almost every parameter value the Hausdorff dimension of the Julia set is the minimum of 2 and the zero of the pressure function. Moreover, the Hausdorff dimension of the exceptional set of parameters is estimated. We also show that if the zero of the pressure function is greater than 2, then typically the 2-dimensional Lebesgue measure of the Julia set is positive. Some sufficient Conditions for a family to satisfy the Transversality Conditions are given. We give non-trivial examples of families of semigroups of non-linear polynomials with Transversality Condition for which the Hausdorff dimension of the Julia set is typically equal to the zero of the pressure function and is less than 2. We also show that a family of small perturbations of Sierpi\'nski gasket system satisfies that for a typical parameter value, the Hausdorff dimension of the Julia set (limit set) is equal to the zero of the pressure function, which is equal to the similarity dimension. Combining the arguments on the Transversality Condition, thermodynamical formalisms and potential theory, we show that for each complex number $a$ with $|a|\neq 0,1$, the family of small perturbations of the semigroup generated by ${z^{2}, az^2} $ satisfies that for a typical parameter value, the 2-dimensional Lebesgue measure of the Julia set is positive.
Junmi Park - One of the best experts on this subject based on the ideXlab platform.
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Stably Limit Shadowing Diffeomorphisms
Abstract and Applied Analysis, 2015Co-Authors: Manseob Lee, Junmi ParkAbstract:Let be a diffeomorphism on a closed surface. In this paper, we show that if has the -stably limit shadowing property, then we have the following: (i) satisfies the Kupka-Smale Condition; (ii) if is dense in the nonwandering set () and if there is a dominated splitting on (), then satisfies both Axiom and the strong Transversality Condition.
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limit shadowing with c 0 Transversality Condition
Journal of the Chungcheong Mathematical Society, 2012Co-Authors: Keonhee Lee, Manseob Lee, Junmi ParkAbstract:Let be an Axiom A difeomorphism of a closed 2- dimensional smooth manifold M: We show that has the limit shadowing property if and only if satisfies the Transversality Condition.
Takashi Kamihigashi - One of the best experts on this subject based on the ideXlab platform.
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necessity of the Transversality Condition for stochastic models with bounded or crra utility
2004Co-Authors: Takashi KamihigashiAbstract:This paper shows that the standard Transversality Condition (STVC) is nec-essary for optimality in stochastic models with bounded or constant-relative-risk- aversion (CRRA) utility under fairly general Conditions. We consider an infinite-horizon stochastic maximization problem that takes a general form of a multi-sector growth model with a single consumption good. We show that the STVC is necessary if utility is bounded or logarithmic. We also show that the STVC is necessary in the case of non-logarithmic CRRA utility as long as lifetime utility is finite at the optimum. These results apply to various stochastic growth models, including real business cycle models with endoge-nous labor supply. Since unbounded utility functions that do not belong to the CRRA class are rather rare in applications, our results provide a fairly complete set of solutions regarding necessity of the STVC in practice.
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necessity of the Transversality Condition for stochastic models with crra utility
2003Co-Authors: Takashi KamihigashiAbstract:This paper shows that the standard Transversality Condition (STVC) is necessary for optimality for stochastic models with constant-relative-risk-aversion (CRRA) utility under general Conditions. We consider an infinite-horizon stochastic maximization problem that takes a general form of multi-sector growth model with a single consumption good and CRRA utility. We establish two results. The first result is that the STVC is necessary in the case of logarithmic utility. The second result is that the STVC is necessary in the case of non-logarithmic CRRA utility as long as lifetime utility is finite at the optimum. These results apply to various stochastic growth models, including real business cycle (RBC) models with endogenous labor supply. Our results make it clear that there is practically no issue about necessity of the STVC for stochastic models with CRRA utility.
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A Simple Proof of the Necessity of the Transversality Condition
SSRN Electronic Journal, 2001Co-Authors: Takashi KamihigashiAbstract:This note provides a simple proof of the necessity of the Transversality Condition for the differentiable reduced-form model. The proof uses only an elementary perturbation argument without relying on dynamic programming. The proof makes it clear that, contrary to common belief, the necessity of the Transversality Condition can be shown in a straightforward way.
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A simple proof of Ekeland and Scheinkman's result on the necessity of a Transversality Condition
Economic Theory, 2000Co-Authors: Takashi KamihigashiAbstract:Ekeland and Scheinkman (1986) prove the necessity of a standard Transversality Condition under certain technical Conditions. Their result is one of the most powerful on the necessity of a Transversality Condition currently available in the literature, and their proof involves numerous estimations and relies on Ekeland's variational principle and Fatou's lemma. This note relaxes some of their assumptions and provides a simple proof that uses neither Ekeland's principle nor a convergence result like Fatou's lemma.
Pierre Cartigny - One of the best experts on this subject based on the ideXlab platform.
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Transversality Condition for singular infinite horizon calculus of variations
Journal of Global Optimization, 2011Co-Authors: Eladio Ocana Anaya, Pierre CartignyAbstract:We consider an optimal infinite horizon calculus of variations problem linear with respect to the velocities. In this framework the Euler---Lagrange equation are known to be algebraic and thus no informative for the general optimal solutions. We prove that the value of the objective along the MRAPs, the curves that connect as quickly as possible the solutions of the Euler---Lagrange equation, is Lipschitz continuous and satisfies a Hamilton---Jacobi equation in some generalised sense. We derive then a sufficient Condition for a MRAP to be optimal by using a Transversality Condition at infinity that we generalize to our non regular context.
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Transversality Condition for singular infinite horizon calculus of variations
Journal of Global Optimization, 2011Co-Authors: Eladio Ocana Anaya, Pierre CartignyAbstract:Infinite horizon, Calculus of variation, MRAP, Hamilton–Jacobi equation, Transversality Condition,
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brief on a sufficient Transversality Condition for infinite horizon optimal control problems
Automatica, 2003Co-Authors: Pierre Cartigny, Philippe MichelAbstract:We prove that, for a class of optimal control problems with infinite horizon, convergence to zero for the co-state variable when time goes to infinity is a sufficient Transversality Condition.
