The paper presents an application of stochastic control methods to fixed income management in an incomplete market with external economic factors. The objective of an investor is the minimization of a shortfall risk. The problem is reduced to the multidimensional Bellman equation. It is shown that for a large class of loss functions the equation possesses a continuous solution. We also consider loss functions from the HARA class and prove that for such functions the Hamilton-Jacobi-Bellman equation has a sufficiently smooth solution. This solution guarantees the existence of a well defined investment strategy. A special example of the bond portfolio with interest rates governed by the Gaussian HJM model is solved explicitly.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc83-0-12,
author = {Andrzej Palczewski},
title = {Risk minimizing strategies for a portfolio of interest-rate securities},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {195-212},
zbl = {1151.93034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc83-0-12}
}
Andrzej Palczewski. Risk minimizing strategies for a portfolio of interest-rate securities. Banach Center Publications, Tome 83 (2008) pp. 195-212. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc83-0-12/