In this paper we investigate novel applications of a new class of equations which we call time-delayed backward stochastic differential equations. We show that many pricing and hedging problems concerning structured products, participating products or variable annuities can be handled by this equations. Time-delayed BSDEs may appear 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  values of the portfolio.  This is usually the case for investment funds or life insurance investment contracts which have bonus distribution mechanisms or provide protection against low returns . We consider some life insurance products, derive the corresponding time-delayed BSDEs and solve them explicitly or at least provide hints how to solve them numerically. We investigate perfect hedging and quadratic hedging which is crucial for insurance applications . 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 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.
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We show that many pricing and hedging problems concerning structured products, participating products or variable annuities can be handled by this equations.
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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.
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investment funds or life insurance investment contracts which have bonus distribution mechanisms or provide protection against low returns
capital protected funds and performance linked pay-offs
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some life insurance products,
pay-offs arising under participating contracts, variable annuities, structured products and hedge funds with hurdle rates and high water marks. We
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We investigate perfect
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which is crucial for insurance applications
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