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November 2002 High-risk and competitive investment models
F. Thomas Bruss, Thomas S. Ferguson
Ann. Appl. Probab. 12(4): 1202-1226 (November 2002). DOI: 10.1214/aoap/1037125860

Abstract

How should we invest capital into a sequence of investment opportunities, if, for reasons of external competition, our interest focuses on trying to invest in the very best opportunity? We introduce new models to answer such questions. Our objective is to formulate them in a way that makes results high-risk specific in order to present true alternatives to other models. At the same time we try to keep them applicable in quite some generality, also for different utility functions. Viewing high-risk situations we assume that an investment on the very best opportunity yields a lucrative, possibly time-dependent, rate of return, that uninvested capital keeps its risk-free value, whereas "wrong" investments lose their value. Several models are presented, mainly for the so-called rank-based case. Optimal strategies and values are found, also for different utility functions, and several examples are explicitly solved. We also include results for the so-called full-information case, where, in addition, the quality distribution of investment opportunities is supposed to be known. In addition we present tractable models for an unknown number of opportunities in terms of Pascal arrival processes. Effort is made throughout the article to justify assumptions in the view of applicability.

Citation

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F. Thomas Bruss. Thomas S. Ferguson. "High-risk and competitive investment models." Ann. Appl. Probab. 12 (4) 1202 - 1226, November 2002. https://doi.org/10.1214/aoap/1037125860

Information

Published: November 2002
First available in Project Euclid: 12 November 2002

zbMATH: 1005.60054
MathSciNet: MR1936590
Digital Object Identifier: 10.1214/aoap/1037125860

Subjects:
Primary: 60G40
Secondary: 90A80

Keywords: Differential equations , Euler--Cauchy approximation , hedging , Kelly betting system , odds-algorithm , Pascal processes , random number of opportunities , secretary problems , Utility

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.12 • No. 4 • November 2002
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