Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management in insurance and finance

Łukasz Delong. "Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management in insurance and finance." Applicationes Mathematicae 39.4 (2012): 463-488. <http://eudml.org/doc/279895>.

@article{ŁukaszDelong2012,
abstract = {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.},
author = {Łukasz Delong},
journal = {Applicationes Mathematicae},
keywords = {backward stochastic differential equations; asset-liability management; participating contracts; variable annuities; capital-protected investments; performance-linked pay-offs},
language = {eng},
number = {4},
pages = {463-488},
title = {Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management in insurance and finance},
url = {http://eudml.org/doc/279895},
volume = {39},
year = {2012},
}

TY - JOUR
AU - Łukasz Delong
TI - Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management in insurance and finance
JO - Applicationes Mathematicae
PY - 2012
VL - 39
IS - 4
SP - 463
EP - 488
AB - 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.
LA - eng
KW - backward stochastic differential equations; asset-liability management; participating contracts; variable annuities; capital-protected investments; performance-linked pay-offs
UR - http://eudml.org/doc/279895
ER -