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

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

2006-10-06

arxiv.org/abs/math/0610224v1

Annals of Applied Probability 2006, Vol. 16, No. 3, 1352-1384

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051606000000259 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051606000000259

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 num\'{e}raire given by the optimal wealth process.

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