Open Access
March 2007 Optimal strategies in high risk investments
Krzysztof Szajowski, Daniel Łebek
Bull. Belg. Math. Soc. Simon Stevin 14(1): 143-155 (March 2007). DOI: 10.36045/bbms/1172852250


A decision-maker observes sequentially a given permutation of $n$ uniquely rankable options. He has to invest capital into these opportunities at the moment when they appear. At each step only relative ranks are known. At the end the true rank of the option, at which the investment has been made, is known. [Bruss and Ferguson] have considered such problems under the assumption that an investment on the very best opportunity yields a lucrative, possibly time-dependent, rate of return. Uninvested capital keeps its risk-free value. Wrong investments lose their value. In this paper we partially extend results by [Bruss and Ferguson]. We confine our study to linear utility but a wider range of payoffs is taken into account. Two cases are considered. The first-type payoff gives a positive rate of return if the investment is made on the best or the second best option. The second-type payoff pays when the investment is at the second best option. We motivate these payoff choices. A few examples are explicitly solved.


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Krzysztof Szajowski. Daniel Łebek. "Optimal strategies in high risk investments." Bull. Belg. Math. Soc. Simon Stevin 14 (1) 143 - 155, March 2007.


Published: March 2007
First available in Project Euclid: 2 March 2007

zbMATH: 1219.91128
MathSciNet: MR2327332
Digital Object Identifier: 10.36045/bbms/1172852250

Primary: 60G40
Secondary: 60K99 , 90A46

Keywords: Differential equations , Euler-Cauchy approximation , hedging , Kelly betting system , secretary problems , Utility

Rights: Copyright © 2007 The Belgian Mathematical Society

Vol.14 • No. 1 • March 2007
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