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.

Non-Concave Utility Maximization without the Concavification Principle

2019 ◽  
Author(s):  
Min Dai ◽  
Steven Kou ◽  
Shuaijie Qian ◽  
Xiangwei Wan
Keyword(s):  
Utility Maximization
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