We model information flows in continuous time that are generated by a number of information sources that are switched on and off at random times. In a novel approach , we explicitly relate the discovery of relevant new information sources to jumps in the conditional expectation process of a partially observed signal. We derive the resulting endogenous jump-diffusion , and show that it is a solution to the stochastic filtering problem associated with the Markov-modulated multivariate information process . We give a Feynman-Ka\'c representation for the endogenous jump-diffusion, and produce an explicit expression for the size of the jumps . The jump-size distribution is a function of a weighted sum of those information processes that are activated at the jump time. The proposed approach can be applied broadly in signal processing, and an example in Mathematical Finance is provided. We consider a vanilla option and find that its Merton-type price can be expressed by a weighted sum of vanilla prices based on the possible combinations of active information processes at option maturity. The constructed information-flow models lend themselves to the quantification of informational advantage in a competition where agents 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 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 information is 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 option can 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.
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information flows in continuous time that are
continuous-time information flows
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By modulating a multi-dimensional information process over a random point field
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the conditional expectation process of a partially observed signal. We derive the resulting endogenous
conditional expectation processes of partially observed signals. We show that the underlying measure-valued process follows
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, and show that it is a solution to the stochastic filtering problem associated with the Markov-modulated multivariate information process . We give a Feynman-Ka\'c representation for the endogenous jump-diffusion, and produce an explicit expression for the size of the jumps . The jump-size distribution is a function of
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 information is
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weighted sum of those information processes that are activated at the jump time. The proposed approach can be applied broadly in signal processing, and an example in Mathematical Finance is provided. We consider a vanilla option and find that its Merton-type price
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 option
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vanilla prices
option values
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combinations of active information processes at option maturity. The constructed information-flow models
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
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in a competition where agents
among competitive agents who