Geodesic
Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management in insurance and finance
Łukasz Delong1
1 Institute of Econometrics Warsaw School of Economics Al. Niepodległości 162 02-554 Warszawa, Poland
Applicationes Mathematicae, Tome 39 (2012) no. 4, pp. 463-488.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/am39-4-5
Keywords: investigate novel applications class equations which call time delayed backward stochastic differential equations time delayed bsdes may arise insurance finance attempt investment strategy investment portfolio which should replicate liability meet target depending strategy applied past values portfolio setting managed investment portfolio serves simultaneously underlying security which liability target contingent replicating portfolio liability target usually capital protected investments performance linked pay offs examples pricing hedging portfolio management problems asset liability management problems which could investigated framework time delayed bsdes focus participating contracts variable annuities believe time delayed bsdes could offer tool studying investment life insurance contracts desirable perspective

Łukasz Delong 1

1 Institute of Econometrics Warsaw School of Economics Al. Niepodległości 162 02-554 Warszawa, Poland 
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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) no. 4, pp. 463-488. doi : 10.4064/am39-4-5. http://geodesic.mathdoc.fr/articles/10.4064/am39-4-5/

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