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Generalization of Kelly's formula You are given one million dollars. Each day you bet x dollars on a coin toss. If a head appears, you get Ax dollars (A > 1); and if a tail appears, you get Bx dollars (B < 1). The head shows up with probability p and the tail shows up with probability 1-p. Please compute the optimal a such that betting a fraction of your wealth each day maximizes the growth of Your wealth

Generalization of Kelly's formula You are given one million dollars. Each day you bet x dollars on a coin toss. If a head appears, you get Ax dollars (A > 1); and if a tail appears, you get Bx dollars (B < 1). The head shows up with probability p and the tail shows up with probability 1-p. Please compute the optimal a such that betting a fraction of your wealth each day maximizes the growth of Your wealth

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Generalization of Kelly's formula You are given one million dollars. Each day you bet x dollars on a coin toss. appears, you get Ax dollars (A > 1); and if a tail appears, you get Bx dollars (B < 1). The head shows up with probability p and the tail shows up with probability 1-p. Please compute the optimal a such that betting a fraction of your wealth each day maximizes the growth of If a head your wealth.
Transcribed Image Text:Generalization of Kelly's formula You are given one million dollars. Each day you bet x dollars on a coin toss. appears, you get Ax dollars (A > 1); and if a tail appears, you get Bx dollars (B < 1). The head shows up with probability p and the tail shows up with probability 1-p. Please compute the optimal a such that betting a fraction of your wealth each day maximizes the growth of If a head your wealth.
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