Solving the consumer’s utility-maximization problem with CES and Cobb-Douglas utility function via mathematical inequalities

2016 ◽  
Vol 11 (4) ◽  
pp. 875-884 ◽  
Author(s):  
Vedran Kojić
Keyword(s):  
Utility Function ◽  
Utility Maximization ◽  
Maximization Problem ◽  
Utility Maximization Problem

scholarly journals UTILITY THEORY FRONT TO BACK — INFERRING UTILITY FROM AGENTS' CHOICES

2014 ◽  
Vol 17 (03) ◽  
pp. 1450018 ◽  
Author(s):  
ALEXANDER M. G. COX ◽  
DAVID HOBSON ◽  
JAN OBłÓJ
Keyword(s):  
Utility Function ◽  
Utility Theory ◽  
Consistency Condition ◽  
Maximization Problem ◽  
Consumption Pattern ◽  
Investment Strategies ◽  
Inverse Approach ◽  
To Come ◽  
Utility Maximization Problem ◽  
Stochastic Setting

We pursue an inverse approach to utility theory and associated consumption and investment problems. Instead of specifying a utility function and deriving the actions of an agent, we assume that we observe the actions of the agent (i.e. consumption and investment strategies) and ask if it is possible to derive a utility function for which the observed behavior is optimal. We work in continuous time both in a deterministic and stochastic setting. In the deterministic setup, we find that there are infinitely many utility functions generating a given consumption pattern. In the stochastic setting of a geometric Brownian motion market it turns out that the consumption and investment strategies have to satisfy a consistency condition (PDE) if they are to come from a classical utility maximization problem. We show further that important characteristics of the agent such as risk attitudes (e.g., DARA) can be deduced directly from the agent's consumption and investment choices.

scholarly journals Dual Formulation of the Utility Maximization Problem Under Transaction Costs

2001 ◽  
Vol 11 (4) ◽  
pp. 1353-1383 ◽  
Author(s):  
Griselda Deelstra ◽  
Huyên Pham ◽  
Nizar Touzi
Keyword(s):  
Transaction Costs ◽  
Utility Maximization ◽  
Maximization Problem ◽  
Dual Formulation ◽  
Utility Maximization Problem

scholarly journals SOLVABILITY AND NUMERICAL SIMULATION OF BSDEs RELATED TO BSPDEs WITH APPLICATIONS TO UTILITY MAXIMIZATION

2011 ◽  
Vol 14 (05) ◽  
pp. 635-667 ◽  
Author(s):  
PETER IMKELLER ◽  
ANTHONY RÉVEILLAC ◽  
JIANING ZHANG
Keyword(s):  
Financial Markets ◽  
Existence And Uniqueness ◽  
Utility Maximization ◽  
Optimization Problem ◽  
Terminal Condition ◽  
Quadratic Growth ◽  
Maximization Problem ◽  
Existence Of A Solution ◽  
Utility Maximization Problem ◽  
Portfolio Optimization Problem

In this paper we study BSDEs arising from a special class of backward stochastic partial differential equations (BSPDEs) that is intimately related to utility maximization problems with respect to arbitrary utility functions. After providing existence and uniqueness we discuss the numerical realizability. Then we study utility maximization problems on incomplete financial markets whose dynamics are governed by continuous semimartingales. Adapting standard methods that solve the utility maximization problem using BSDEs, we give solutions for the portfolio optimization problem which involve the delivery of a liability at maturity. We illustrate our study by numerical simulations for selected examples. As a byproduct we prove existence of a solution to a very particular quadratic growth BSDE with unbounded terminal condition. This complements results on this topic obtained in Briand and Hu (2006, 2008) and Briand et al. (2007).

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