We model continuous-time information flows generated by a number of information sources that switch on and off at random times. By modulating a multi-dimensional information process over a random point field, we explicitly relate the discovery of relevant new information sources to jumps in conditional expectation processes of partially observed signals. We show that the underlying measure-valued process follows jump-diffusion dynamics, where the jumps are governed by information source switches. The dynamic representation gives rise to a set of martingales on random time intervals that capture evolving information states  as well as to a state-dependent stochastic volatility evolution with jumps. The nature of information flows usually exhibits complex behaviour, however, we succeed in maintaining analytic tractability by introducing what we term the effective and complementary information processes . The effective information captures in a univariate process all information provided by the active sources, and the complementary informationis a function-valued stochastic process which is constant between changes of states. One of the many potential applications is in finance: we associate the signal to a random payoff and price a financial derivative within the modulated information approach. It turns out that the price of a vanilla optioncan be expressed by a weighted sum of option values based on the possible state configurations at option expiry. This result may be viewed as an information-based analogue of Merton's option price, but where jump-diffusion arises endogenously. The proposed information flow models also lend themselves to the quantification of  informational advantage among competitive agents who have asymmetric information flows .
We model continuous-time information flows generated by a number of information sources that switch on and off at random times. By modulating a multi-dimensional L\'evy random bridge over a random point field, our framework relates the discovery of relevant new information sources to jumps in conditional expectation martingales. In the canonical Brownian random bridge case, we show that the underlying measure-valued process follows jump-diffusion dynamics, where the jumps are governed by information switches. The dynamic representation gives rise to a set of stochastically-linked Brownian motions on random time intervals that capture evolving information states , as well as to a state-dependent stochastic volatility evolution with jumps. The nature of information flows usually exhibits complex behaviour, however, we maintain analytic tractability by introducing what we term the effective and complementary information processes , which dynamically incorporate active and inactive information, respectively. As an application, we price a financial vanilla option, which we prove is expressed by a weighted sum of option values based on the possible state configurations at expiry. This result may be viewed as an information-based analogue of Merton's option price, but where jump-diffusion arises endogenously. The proposed information flows also lend themselves to the quantification of asymmetric informational advantage among competitive agents , a feature we analyse by notions of information geometry .
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information process
L\'evy random bridge
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we explicitly relate
our framework relates
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processes of partially observed signals. We
martingales. In the canonical Brownian random bridge case, we
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source
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martingales
stochastically-linked Brownian motions
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,
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succeed in maintaining
maintain
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. The effective information captures in a univariate process all information provided by the active sources, and the complementary informationis a function-valued stochastic process which is constant between changes of states. One of the many potential applications is in finance: we associate the signal to a random payoff and
, which dynamically incorporate active and inactive information, respectively. As an application, we
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derivative within the modulated information approach. It turns out that the price of a vanilla optioncan be
vanilla option, which we prove is
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option
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flow models
flows
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asymmetric
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who have asymmetric information flows
, a feature we analyse by notions of information geometry