In this paper we consider backward stochastic differential equations with time-delayed generators of a moving average type. The classical and well-known framework with linear generators depending on (Y(t),Z(t)) is extended and we investigate linear generators depending on (1{t}\int_0^tY(s)ds, 1{t}\int_0^tZ(s)ds). This seems to be a natural step forward in the study of BSDEs. We derive explicit solutions to the corresponding time-delayed BSDEs and we investigate in detail some properties of the solutions. In particular, these solutions are linear, time-consistent, continuous, non-monotonic and not conditionally invariant with respect to a terminal condition. A motivation for dealing with generators of a moving average type in the context of dynamic pricing and recursive utilities is given. We propose a new direction in modelling of investors' preferencesand behaviors .
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 (1{t}\int_0^tY(s)ds, 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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in the context of dynamic pricing and recursive utilities
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propose a new direction in modelling of investors' preferencesand behaviors
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