## The Annals of Applied Probability

### On the two-times differentiability of the value functions in the problem of optimal investment in incomplete markets

#### Abstract

We study the two-times differentiability of the value functions of the primal and dual optimization problems that appear in the setting of expected utility maximization in incomplete markets. We also study the differentiability of the solutions to these problems with respect to their initial values. We show that the key conditions for the results to hold true are that the relative risk aversion coefficient of the utility function is uniformly bounded away from zero and infinity, and that the prices of traded securities are sigma-bounded under the numéraire given by the optimal wealth process.

#### Article information

Source
Ann. Appl. Probab., Volume 16, Number 3 (2006), 1352-1384.

Dates
First available in Project Euclid: 2 October 2006

https://projecteuclid.org/euclid.aoap/1159804984

Digital Object Identifier
doi:10.1214/105051606000000259

Mathematical Reviews number (MathSciNet)
MR2260066

Zentralblatt MATH identifier
1149.91035

Subjects
Primary: 90A09 90A10
Secondary: 90C26: Nonconvex programming, global optimization

#### Citation

Kramkov, Dmitry; Sîrbu, Mihai. On the two-times differentiability of the value functions in the problem of optimal investment in incomplete markets. Ann. Appl. Probab. 16 (2006), no. 3, 1352--1384. doi:10.1214/105051606000000259. https://projecteuclid.org/euclid.aoap/1159804984

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