In this paper we investigate novel applications of a new class of equations which we call time-delayed backward stochastic differential equations. Time-delayed BSDEs may arise  when we want to find a strategy and a portfolio which should replicate the liability whose pay-off depends on the applied investment strategy or the past values of the portfolio. In our setting, an investment portfolio serves simultaneously as the underlying security on which the liability  is contingent and as a hedge portfolio for the liability . This is usually the case for capital protected funds and performance linked pay-offs. We consider pay-offs arising under participating contracts , variable annuities, structured products and hedge funds with hurdle rates and high water marks . We derive the corresponding time-delayed BSDEs and solve them explicitly or at least provide hints how to solve them numerically. Perfect hedging and quadratic hedging are investigated. We study consequences and give an economic interpretation of the  fact that a time-delay BSDE may not have a solution or may have multiple solutions.
In this paper 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 finance when we want to find an investment strategy and an investment portfolio which should replicate a liability or meet a target depending on the applied strategy 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 for 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. Our motivation comes from life insurance and we focus on participating contracts and variable annuities . We derive the corresponding time-delayed BSDEs and solve them explicitly or at least provide hints how to solve them numerically. We give a financial interpretation of the theoretical fact that a time-delayed BSDE may not have a solution or may have multiple solutions.
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in finance
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a strategy and a
an investment strategy and an investment
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the liability whose pay-off depends
a liability or meet a target depending
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investment
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our setting, an
this setting, a managed
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/target
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hedge portfolio for the liability
replicating portfolio for that liability/target
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capital protected funds and performance linked
capital-protected investments and performance-linked
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consider pay-offs arising under participating contracts , variable annuities, structured products and hedge funds with hurdle rates and high water marks
give examples of pricing, hedging and portfolio management problems (asset-liability management problems) which could be investigated in the framework of time-delayed BSDEs. Our motivation comes from life insurance and we focus on participating contracts and variable annuities
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Perfect hedging and quadratic hedging are investigated. We study consequences and give an economic
We give a financial
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theoretical
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time-delay
time-delayed