In this paper we consider a new class of dynamic pricing principles and recursive utilities. We start with the interpretation of the generator of a backward stochastic differential equation as an infinitesimal pricing rule or an instantaneous utility. With this interpretation the generator has an economic meaning and describes the subjective views of the investor concerning the expected change in the price or the utility. We give a motivation for considering non-Markovian generators of BSDEs which leads us to{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 so-called time-delayed backward stochastic differential equations. We investigate two pricing principles and recursive utilities which are derived from time-delayed BSDEs with generators of a moving average type . They might be useful in the case of an individual valuation of a pay-off. A non-Markovian generator arises when the local valuation rule of the investor depends on the past values of prices, volatilities or utilities. Some properties of our new pricing principles and recursive utilities are considered and we show that they are fundamentally different from the properties which hold for prices and utilities based on classical BSDEs. An interpretation of this fact is provided .
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 (\frac{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' preferences and behaviors .
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a new class of dynamic pricing principles and recursive utilities. We start with the interpretation of the generator of a
R
equation as an infinitesimal pricing rule or an instantaneous utility. With this interpretation the generator has an economic meaning and describes the subjective views of the investor concerning the expected change in the price or the utility. We give a motivation for considering non-Markovian generators of BSDEs which leads us to
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 (\frac{1
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so-called
BSDEs. We derive explicit solutions to the corresponding
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backward stochastic differential equations. We investigate two pricing principles and recursive utilities which are derived from time-delayed
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with
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
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. They might be useful in the case of an individual valuation of a pay-off. A non-Markovian generator arises when the local valuation rule of the investor depends on the past values of prices, volatilities or utilities. Some properties of our new pricing principles
in the context of dynamic pricing
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are considered and we show that they are fundamentally different from the properties which hold for prices and utilities based on classical BSDEs. An interpretation of this fact is provided
is given. We propose a new direction in modelling of investors' preferences and behaviors