Arbitrage and utility maximization in market models with an insider

Huy N. Chau; Wolfgang J. Runggaldier; Peter Tankov

doi:10.1007/s11579-018-0217-4

Arbitrage and utility maximization in market models with an insider

Huy N. Chau
, Wolfgang J. Runggaldier
, Peter Tankov

Research output: Contribution to journal › Article › peer-review

Abstract

We study arbitrage opportunities, market viability and utility maximization in market models with an insider. Assuming that an economic agent possesses an additional information in the form of an F_T-measurable discrete random variable G, we give criteria for the no unbounded profits with bounded risk property to hold, characterize optimal arbitrage strategies, and prove duality results for the utility maximization problem faced by the insider. Examples of markets satisfying NUPBR yet admitting arbitrage opportunities are provided. For the case when G is a continuous random variable, we consider the notion of no asymptotic arbitrage of the first kind (NAA1) and give an explicit construction for unbounded profits if NAA1 fails.

Original language	English
Pages (from-to)	589-614
Number of pages	26
Journal	Mathematics and Financial Economics
Volume	12
Issue number	4
DOIs	https://doi.org/10.1007/s11579-018-0217-4
Publication status	Published - 1 Sept 2018

Keywords

Hedging
Incomplete markets
Initial enlargement of filtration
No unbounded profits with bounded risk
Optimal arbitrage
Utility maximization

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10.1007/s11579-018-0217-4

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title = "Arbitrage and utility maximization in market models with an insider",

abstract = "We study arbitrage opportunities, market viability and utility maximization in market models with an insider. Assuming that an economic agent possesses an additional information in the form of an FT-measurable discrete random variable G, we give criteria for the no unbounded profits with bounded risk property to hold, characterize optimal arbitrage strategies, and prove duality results for the utility maximization problem faced by the insider. Examples of markets satisfying NUPBR yet admitting arbitrage opportunities are provided. For the case when G is a continuous random variable, we consider the notion of no asymptotic arbitrage of the first kind (NAA1) and give an explicit construction for unbounded profits if NAA1 fails.",

keywords = "Hedging, Incomplete markets, Initial enlargement of filtration, No unbounded profits with bounded risk, Optimal arbitrage, Utility maximization",

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AU - Chau, Huy N.

AU - Runggaldier, Wolfgang J.

AU - Tankov, Peter

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N2 - We study arbitrage opportunities, market viability and utility maximization in market models with an insider. Assuming that an economic agent possesses an additional information in the form of an FT-measurable discrete random variable G, we give criteria for the no unbounded profits with bounded risk property to hold, characterize optimal arbitrage strategies, and prove duality results for the utility maximization problem faced by the insider. Examples of markets satisfying NUPBR yet admitting arbitrage opportunities are provided. For the case when G is a continuous random variable, we consider the notion of no asymptotic arbitrage of the first kind (NAA1) and give an explicit construction for unbounded profits if NAA1 fails.

AB - We study arbitrage opportunities, market viability and utility maximization in market models with an insider. Assuming that an economic agent possesses an additional information in the form of an FT-measurable discrete random variable G, we give criteria for the no unbounded profits with bounded risk property to hold, characterize optimal arbitrage strategies, and prove duality results for the utility maximization problem faced by the insider. Examples of markets satisfying NUPBR yet admitting arbitrage opportunities are provided. For the case when G is a continuous random variable, we consider the notion of no asymptotic arbitrage of the first kind (NAA1) and give an explicit construction for unbounded profits if NAA1 fails.

KW - Hedging

KW - Incomplete markets

KW - Initial enlargement of filtration

KW - No unbounded profits with bounded risk

KW - Optimal arbitrage

KW - Utility maximization

U2 - 10.1007/s11579-018-0217-4

DO - 10.1007/s11579-018-0217-4

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SN - 1862-9679

VL - 12

SP - 589

EP - 614

JO - Mathematics and Financial Economics

JF - Mathematics and Financial Economics

IS - 4

ER -

Arbitrage and utility maximization in market models with an insider

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Keywords

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