2 research outputs found
Sensitivity analysis of utility-based prices and risk-tolerance wealth processes
In the general framework of a semimartingale financial model and a utility
function defined on the positive real line, we compute the first-order
expansion of marginal utility-based prices with respect to a ``small'' number
of random endowments. We show that this linear approximation has some important
qualitative properties if and only if there is a risk-tolerance wealth process.
In particular, they hold true in the following polar cases:
\begin{tabular}@p97mm@ for any utility function , if and only if the set of
state price densities has a greatest element from the point of view of
second-order stochastic dominance;for any financial model, if and only if
is a power utility function ( is an exponential utility function if it is
defined on the whole real line). \end{tabular}Comment: Published at http://dx.doi.org/10.1214/105051606000000529 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
On the two-times differentiability of the value functions in the problem of optimal investment in incomplete markets
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.Comment: Published at http://dx.doi.org/10.1214/105051606000000259 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org