Optimality conditions for utility maximization in an incomplete market

2008 ◽  
pp. 3-23 ◽  
Author(s):  
Ioannis Karatzas ◽  
John P. Lehoczky ◽  
Steven E. Shreve ◽  
Gan-Lin Xu
Keyword(s):  
Optimality Conditions ◽  
Utility Maximization ◽  
Incomplete Market

Martingale and Duality Methods for Utility Maximization in an Incomplete Market

1991 ◽  
Vol 29 (3) ◽  
pp. 702-730 ◽  
Author(s):  
Ioannis Karatzas ◽  
John P. Lehoczky ◽  
Steven E. Shreve ◽  
Gan-Lin Xu
Keyword(s):  
Utility Maximization ◽  
Incomplete Market ◽  
Duality Methods

scholarly journals Optimal investment with intermediate consumption under no unbounded profit with bounded risk

2017 ◽  
Vol 54 (3) ◽  
pp. 710-719 ◽  
Author(s):  
Huy N. Chau ◽  
Andrea Cosso ◽  
Claudio Fontana ◽  
Oleksii Mostovyi
Keyword(s):  
Utility Maximization ◽  
Optimal Investment ◽  
Incomplete Market ◽  
Value Functions ◽  
Stochastic Field ◽  
Intermediate Consumption ◽  
Bounded Risk ◽  
Primal And Dual

Abstract We consider the problem of optimal investment with intermediate consumption in a general semimartingale model of an incomplete market, with preferences being represented by a utility stochastic field. We show that the key conclusions of the utility maximization theory hold under the assumptions of no unbounded profit with bounded risk and of the finiteness of both primal and dual value functions.

scholarly journals Kim and Omberg Revisited: The Duality Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Anna Battauz ◽  
Marzia De Donno ◽  
Alessandro Sbuelz
Keyword(s):  
Expected Utility ◽  
Explicit Solution ◽  
Utility Maximization ◽  
Optimal Investment ◽  
Incomplete Market ◽  
Maximization Problem ◽  
Expected Utility Maximization ◽  
Duality Approach ◽  
Utility Maximization Problem ◽  
Optimal Investment Problem

We give an alternative duality-based proof to the solution of the expected utility maximization problem analyzed by Kim and Omberg. In so doing, we also provide an example of incomplete-market optimal investment problem for which the duality approach is conducive to an explicit solution.

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

Analysis and design of thermo-mechanical interfaces

2012 ◽  
Vol 60 (2) ◽  
pp. 205-213
Author(s):  
K. Dems ◽  
Z. Mróz
Keyword(s):  
Optimality Conditions ◽  
Mechanical Loading ◽  
Material Properties ◽  
Structural Response ◽  
External Boundary ◽  
Mechanical Loads ◽  
Internal Interface ◽  
Analysis And Design ◽  
First Order ◽  
Mechanical Nature

Abstract. An elastic structure subjected to thermal and mechanical loading with prescribed external boundary and varying internal interface is considered. The different thermal and mechanical nature of this interface is discussed, since the interface form and its properties affect strongly the structural response. The first-order sensitivities of an arbitrary thermal and mechanical behavioral functional with respect to shape and material properties of the interface are derived using the direct or adjoint approaches. Next the relevant optimality conditions are formulated. Some examples illustrate the applicability of proposed approach to control the structural response due to applied thermal and mechanical loads.

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