scholarly journals Optimal consumption of multiple goods in incomplete markets

2018 ◽  
Vol 55 (3) ◽  
pp. 810-822
Author(s):  
Oleksii Mostovyi
Keyword(s):  
Closed Form ◽  
Incomplete Markets ◽  
Existence And Uniqueness ◽  
Dual Problem ◽  
Optimal Consumption ◽  
Closed Form Solutions ◽  
Uniqueness Of The Solution ◽  
Incomplete Models

Abstract We consider the problem of optimal consumption of multiple goods in incomplete semimartingale markets. We formulate the dual problem and identify conditions that allow for the existence and uniqueness of the solution, and provide a characterization of the optimal consumption strategy in terms of the dual optimizer. We illustrate our results with examples in both complete and incomplete models. In particular, we construct closed-form solutions in some incomplete models.

Structure Design, Kinematics and Grasp Constraint of a Metamorphic Robotic Hand for Meat Deboning Operation

2013 ◽  
Author(s):  
Guowu Wei ◽  
Vahid Aminzadeh ◽  
Evangelos Emmanouil ◽  
Jian S. Dai
Keyword(s):  
Closed Form ◽  
Structure Design ◽  
Robotic Hand ◽  
Meat Industry ◽  
Sensor Systems ◽  
Level Control ◽  
Closed Form Solutions ◽  
Low Level ◽  
Structure And Design

A four-fingered metamorphic robotic hand with a reconfigurable palm is presented in this paper with the application in deboning operation of meat industry. This robotic hand has a reconfigurable palm that generates changeable topology and augments dexterity and versatility for the hand. Mechanical structure and design of the robotic hand are presented and based on mechanism decomposition, kinematics of the metamorphic hand is investigated with closed-form solutions leading to the workspace characterization of the robotic hand. Based on the kinematics of the four-fingered metamorphic hand, utilizing product-of-exponentials formula, grasp map and grasp constraint of the hand are then formulated revealing the grasp robustness and manipulability performed by the metamorphic hand. A prototype of the four-fingered metamorphic hand is consequently fabricated and integrated with low level control and sensor systems leading to a scenario of applying the hand in the field of meat industry for deboning operation.

Stresses in Multilayered Ceramics Subjected to Biaxial Flexure Tests

2008 ◽  
Vol 606 ◽  
pp. 79-92 ◽  
Author(s):  
C.H. Hsueh
Keyword(s):  
Solid Oxide Fuel Cells ◽  
Closed Form ◽  
Analytical Description ◽  
Test Methods ◽  
Standard Test ◽  
Fracture Load ◽  
Closed Form Solutions ◽  
American Society ◽  
Biaxial Flexure

Although standard test methods for biaxial strength measurements of ceramics have been established and the corresponding formulas for relating the biaxial strength to the fracture load have been approved by American Society for Testing and Materials (ASTM) and International Organization for Standardization, respectively, they are limited to the case of monolayered discs. Despite the increasing applications of multilayered ceramics, characterization of their strengths using biaxial flexure tests has been difficult because the analytical description of the relation between the strength and the fracture load for multilayers subjected to biaxial flexure tests is unavailable until recently. Using ring-on-ring tests as an example, the closed-form solutions for stresses in (i) monolayered discs based on ASTM formulas, (ii) bilayered discs based on Roark’s formulas, and (iii) multilayered discs based on Hsueh et al.’s formulas are reviewed in the present study. Finite element results for ring-on-rings tests performed on (i) zirconia monolayered discs, (ii) dental crown materials of porcelain/zirconia bilayered discs, and (iii) solid oxide fuel cells trilayered discs are also presented to validate the closed-form solutions. With Hsueh et al.’s formulas, the biaxial strength of multilayered ceramics can be readily evaluated using biaxial flexure tests.

scholarly journals OPTIMAL CONSUMPTION AND INVESTMENT IN INCOMPLETE MARKETS WITH GENERAL CONSTRAINTS

2011 ◽  
Vol 11 (02n03) ◽  
pp. 283-299 ◽  
Author(s):  
PATRICK CHERIDITO ◽  
YING HU
Keyword(s):  
Incomplete Markets ◽  
Existence And Uniqueness ◽  
Quadratic Growth ◽  
Optimal Consumption ◽  
Explicit Solutions ◽  
Uniqueness Of Solutions ◽  
Power Utility ◽  
General Constraints ◽  
Stochastic Constraints ◽  
Optimal Consumption And Investment

We study an optimal consumption and investment problem in a possibly incomplete market with general, not necessarily convex, stochastic constraints. We provide explicit solutions for investors with exponential, logarithmic as well as power utility and show that they are unique if the constraints are convex. Our approach is based on martingale methods that rely on results on the existence and uniqueness of solutions to BSDEs with drivers of quadratic growth.

scholarly journals Entropy-regularized 2-Wasserstein distance between Gaussian measures

2021 ◽  
Author(s):  
Anton Mallasto ◽  
Augusto Gerolin ◽  
Hà Quang Minh
Keyword(s):  
Fixed Point ◽  
Closed Form ◽  
Numerical Study ◽  
Wasserstein Distance ◽  
Iteration Algorithm ◽  
Probability Measures ◽  
Gaussian Distributions ◽  
Closed Form Solutions ◽  
Special Cases

AbstractGaussian distributions are plentiful in applications dealing in uncertainty quantification and diffusivity. They furthermore stand as important special cases for frameworks providing geometries for probability measures, as the resulting geometry on Gaussians is often expressible in closed-form under the frameworks. In this work, we study the Gaussian geometry under the entropy-regularized 2-Wasserstein distance, by providing closed-form solutions for the distance and interpolations between elements. Furthermore, we provide a fixed-point characterization of a population barycenter when restricted to the manifold of Gaussians, which allows computations through the fixed-point iteration algorithm. As a consequence, the results yield closed-form expressions for the 2-Sinkhorn divergence. As the geometries change by varying the regularization magnitude, we study the limiting cases of vanishing and infinite magnitudes, reconfirming well-known results on the limits of the Sinkhorn divergence. Finally, we illustrate the resulting geometries with a numerical study.

scholarly journals Polynomial Approximation on Unbounded Subsets, Markov Moment Problem and Other Applications

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1654
Author(s):  
Octav Olteanu
Keyword(s):  
Polynomial Approximation ◽  
Quadratic Forms ◽  
Existence And Uniqueness ◽  
Cartesian Product ◽  
Point Of View ◽  
Bounded Linear ◽  
Uniqueness Of The Solution ◽  
Markov Moment ◽  
Unbounded Intervals

This paper starts by recalling the author’s results on polynomial approximation over a Cartesian product A of closed unbounded intervals and its applications to solving Markov moment problems. Under natural assumptions, the existence and uniqueness of the solution are deduced. The characterization of the existence of the solution is formulated by two inequalities, one of which involves only quadratic forms. This is the first aim of this work. Characterizing the positivity of a bounded linear operator only by means of quadratic forms is the second aim. From the latter point of view, one solves completely the difficulty arising from the fact that there exist nonnegative polynomials on ℝn, n≥2, which are not sums of squares.

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