Optimizing Logarithmic Utility: Probing Expected Gains through Anticipative Information in a Brownian-Poisson Market

D'Auria Bernardo, Università di Padova

This talk explores the concept of anticipative information in financial markets, focusing on future events' disclosure, especially in the context of financial assets and their trends. Assuming a market with risky asset dynamics following a Brownian motion and a Poisson process, we employ Malliavin calculus and filtration enlargement techniques to derive the information drift for these processes. We then provide numerous examples demonstrating how to exploit anticipative information about conditions that the constituent processes or their running maximum may verify, by modelling them as non-adapted Bernoulli random variables.

Area: CS30 - Fractional processes and Malliavin calculus for stochastic models (Enrica Pirozzi)

Keywords: enlargement of filtrations; portfolio optimization; Malliavin calculus

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