Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155394 | Stochastic Processes and their Applications | 2016 | 19 Pages |
Abstract
In the problem of optimal investment with a utility function defined on (0,∞)(0,∞), we formulate sufficient conditions for the dual optimizer to be a uniformly integrable martingale. Our key requirement consists of the existence of a martingale measure whose density process satisfies the probabilistic Muckenhoupt (Ap)(Ap) condition for the power p=1/(1−a)p=1/(1−a), where a∈(0,1)a∈(0,1) is a lower bound on the relative risk-aversion of the utility function. We construct a counterexample showing that this (Ap)(Ap) condition is sharp.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Dmitry Kramkov, Kim Weston,