Differentiability of the Value Function in the Robust Utility Maximization Problem

2012 ◽  
Vol 56 (2) ◽  
pp. 327-337
Author(s):  
I. S. Morozov
Keyword(s):  
Utility Maximization ◽  
Value Function ◽  
Maximization Problem ◽  
Robust Utility Maximization ◽  
Utility Maximization Problem ◽  
The Value Function

RECURSIVE BACKWARD SCHEME FOR THE SOLUTION OF A BSDE WITH A NON LIPSCHITZ GENERATOR

2017 ◽  
Vol 31 (2) ◽  
pp. 207-225
Author(s):  
Paola Tardelli
Keyword(s):  
Unique Solution ◽  
Financial Market ◽  
Utility Maximization ◽  
Value Function ◽  
Jump Processes ◽  
Maximization Problem ◽  
Admissible Strategies ◽  
Incomplete Financial Market ◽  
Utility Maximization Problem ◽  
The Value Function

On an incomplete financial market, the stocks are modeled as pure jump processes subject to defaults. The exponential utility maximization problem is investigated characterizing the value function in term of Backward Stochastic Differential Equations (BSDEs), driven by pure jump processes. In general, in this setting, there is no unique solution. This is the reason why, the value function is proven to be the limit of a sequence of processes. Each of them is the solution of a Lipschitz BSDE and it corresponds to the value function associated with a subset of bounded admissible strategies. Given a representation of the jump processes driving the model, the aim of this note is to give a recursive backward scheme for the value function of the initial problem.

On the properties of dynamic value functions in the problem of optimal investment in incomplete markets

2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Michael Mania ◽  
Revaz Tevzadze
Keyword(s):  
Incomplete Markets ◽  
Real Line ◽  
Value Function ◽  
Optimal Solution ◽  
Optimal Investment ◽  
Maximization Problem ◽  
Value Functions ◽  
Utility Maximization Problem ◽  
The Value Function ◽  
Uniformly Bounded

AbstractWe study the analytical properties of a dynamic value function and of an optimal solution to the utility maximization problem in incomplete markets for utility functions defined on the whole real line. It was shown by Kramkov and Sirbu [Ann. Appl. Probab. 16 (2006), no. 3, 1352–1384] that if the relative risk-aversion coefficient of the utility function defined on the half real line is uniformly bounded away from zero and infinity, then the value function at time

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
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