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Insider information and its relation with the arbitrage condition and the utility maximization problem
Bernardo D'Auria1, José Antonio Salmerón1
1Department of Statistics, Madrid University Carlos III, Avenida de la Universidad 30, 28911 Leganés, Madrid (Spain).
Mathematical Biosciences and Engineering : MBE
|April 3, 2020
Summary
Insider information in financial portfolio optimization can be valuable but may not always guarantee arbitrage opportunities. This study explores the bounded value of insider knowledge under specific utility functions and bankruptcy constraints.
Area of Science:
- Quantitative Finance
- Financial Economics
- Investment Theory
Background:
- Financial portfolio optimization is a cornerstone of investment strategy.
- The interplay between arbitrage conditions and utility maximization is critical.
- Insider information introduces complexities into traditional financial models.
Purpose of the Study:
- To analyze the relationship between arbitrage and utility maximization with insider information.
- To investigate the impact of future information on portfolio optimization.
- To examine utility maximization under logarithmic and Constant Relative Risk Aversion (CRRA) utilities, with and without no-temporary-bankruptcy constraints.
Main Methods:
- Mathematical modeling of financial portfolio optimization.
- Analysis of utility maximization problems incorporating insider information.
- Application of logarithmic and CRRA utility functions.
- Inclusion of no-temporary-bankruptcy restrictions.
Main Results:
- The value of insider information can be bounded even when arbitrage conditions hold.
- Insider information does not invariably lead to arbitrage opportunities for the insider.
- An explicit example demonstrates that insider information does not always imply arbitrage.
Conclusions:
- The presence of insider information does not automatically create an arbitrage advantage.
- The value derived from insider knowledge in portfolio optimization is subject to specific constraints and conditions.
- Further research can explore the precise boundaries and implications of insider trading in various financial contexts.
Keywords:
No Free Lunch Vanishing Riskarbitrageenlargement of filtrationoptimal portfoliorisk neutral measurevalue of the informationMore Related Videos
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