We investigate novel applications of a new class of equations which we call time-delayed backward stochastic differential equations. Time-delayed BSDEs may arise in insurance and finance in an attempt to find an investment strategy and an investment portfolio which should replicate a liability or meet a target depending on the strategy applied or the past values of the portfolio. In this setting, a managed investment portfolio serves simultaneously as the underlying security on which the liability/target is contingent and as a replicating portfolio for that liability/target. This is usually the case of capital-protected investments and performance-linked pay-offs. We give examples of pricing, hedging and portfolio management problems (asset-liability management problems) which could be investigated in the framework of time-delayed BSDEs. We focus on participating contracts and variable annuities. We believe that time-delayed BSDEs could offer a tool for studying investment life insurance contracts from a new and desirable perspective.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am39-4-5,
author = {\L ukasz Delong},
title = {Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management in insurance and finance},
journal = {Applicationes Mathematicae},
volume = {39},
year = {2012},
pages = {463-488},
zbl = {1254.49024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-4-5}
}
Łukasz Delong. Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management in insurance and finance. Applicationes Mathematicae, Tome 39 (2012) pp. 463-488. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-4-5/