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BSDEs with time-delayed generators of a moving average type with applications to non-monotone preferences

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  • {\L}ukasz Delong
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    Abstract

    In this paper we consider backward stochastic differential equations with time-delayed generators of a moving average type. The classical framework with linear generators depending on $(Y(t),Z(t))$ is extended and we investigate linear generators depending on $(\frac{1}{t}\int_0^tY(s)ds, \frac{1}{t}\int_0^tZ(s)ds)$. We derive explicit solutions to the corresponding time-delayed BSDEs and we investigate in detail main properties of the solutions. An economic motivation for dealing with the BSDEs with the time-delayed generators of the moving average type is given. We argue that such equations may arise when we face the problem of dynamic modelling of non-monotone preferences. We model a disappointment effect under which the present pay-off is compared with the past expectations and a volatility aversion which causes the present pay-off to be penalized by the past exposures to the volatility risk.

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    File URL: http://arxiv.org/pdf/1008.3722
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1008.3722.

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    Date of creation: Aug 2010
    Date of revision: Jul 2011
    Handle: RePEc:arx:papers:1008.3722

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    Web page: http://arxiv.org/

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