We consider an incomplete market with an untradable stochastic factor and a robust investment problem based on the CARA utility. We formulate it as a stochastic differential game problem, and use Hamilton-Jacobi-Bellman-Isaacs equations to derive an explicit representation of the robust optimal portfolio; the HJBI equation is transformed using a substitution of the Cole-Hopf type. Not only the pure investment problem, but also a problem of robust hedging is taken into account: an agent tries to hedge the risk associated with derivatives based on the stochastic factor.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am37-2-6,
author = {Dariusz Zawisza},
title = {Robust portfolio selection under exponential preferences},
journal = {Applicationes Mathematicae},
volume = {37},
year = {2010},
pages = {215-230},
zbl = {1247.91175},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am37-2-6}
}
Dariusz Zawisza. Robust portfolio selection under exponential preferences. Applicationes Mathematicae, Tome 37 (2010) pp. 215-230. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am37-2-6/