A free-model characterization of the asymptotic certainty equivalent by the Arrow-Pratt index. (English) Zbl 1427.91233
Yin, George (ed.) et al., Modeling, stochastic control, optimization, and applications. Selected papers based on invited talks given at the IMA workshop in modeling, stochastic control, optimization, and related applications, Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, MN, USA, May 1 – June 30, 2018. Cham: Springer. IMA Vol. Math. Appl. 164, 261-281 (2019).
Summary: This work concerns with the asymptotic behavior of the optimal wealth process, measured through the certainty equivalent of utility functions with convergent Arrow-Pratt risk aversion index, which we call regular. It is proved that, when the time horizon converges to infinity, the value function is independent of the initial capital. Moreover, when the performance is measured by another regular utility function with the same asymptotic Arrow-Pratt risk aversion index, the constant optimal value is the same, and the sets of optimal investment strategies coincide. Interestingly, these results do not depend on a model specification.
For the entire collection see [Zbl 1418.93005].
For the entire collection see [Zbl 1418.93005].
