Ratio of price to expectation and complete Bernstein functions

Details Ratio of price to expectation and complete Bernstein functions Ratio of price to expectation and complete Bernstein functions

2007-03-03

arxiv.org/abs/math/0703077v1

Mathematics

Optimization and Control

15 pages

Scientific paper

For a game with positive expectation and some negative profit, a unique price exists, at which the optimal proportion of investment reaches its maximum. For a game with parallel translated profit, the ratio of this price to its expectation tends to converge toward less than or equal to 1/2 if its expectation converges to 0. In this paper, we will investigate such properties by using the integral representations of a complete Bernstein function and establish several Abelian and Tauberian theorems.

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