# Ratio of price to expectation and complete Bernstein functions

Research paper by Yukio Hirashita

Indexed on: 02 Mar '07Published on: 02 Mar '07Published in: Mathematics - Optimization and Control

#### Abstract

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.