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Insider information and its relation with the arbitrage condition and the utility maximization problem

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2019-11
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AIMS Press
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Abstract
Within the well-known framework of financial portfolio optimization, we analyze the existing relationships between the condition of arbitrage and the utility maximization in presence of insider information. We assume that, since the initial time, the information flow is altered by adding the knowledge of an additional random variable including future information. In this context we study the utility maximization problem under the logarithmic and the Constant Relative Risk Aversion (CRRA) utilities, with and without the restriction of no temporary-bankruptcy.In particular, we show that the value of the insider information may be bounded while the arbitrage condition holds and we prove that the insider information does not always imply arbitrage for the insider by providing an explicit example.
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Correction: Mathematical Biosciences and Engineering, 20(5), 8305-8307. https://doi.org/10.3934/mbe.2023362 We prove that Theorem 4.16 in [1] is false by constructing a strategy that generates (FLVR) H(G). However, we success to prove that the no arbitrage property still holds when the agent only plays with strategies belonging to the admissible set called buy-and-hold.
Keywords
Optimal portfolio, Enlargement of filtration, Value of the information, Arbitrage, No free lunch vanishing risk, Risk neutral measure
Bibliographic citation
D’Auria, B., & Salmerón, J. A. (2019). Insider information and its relation with the arbitrage condition and the utility maximization problem. Mathematical Biosciences and Engineering, 17(2), 998-1019.