Published online by Cambridge University Press: 05 June 2012
Introduction
In this chapter we consider some optimization problems involving one-time investments not necessarily tied to the movement of a publicly traded security. Section 10.2 introduces a deterministic optimization problem where the objective is to determine an efficient algorithm for finding the optimal investment strategy when a fixed amount of money is to be invested in integral amounts among n projects, each having its own return function. Section 10.2.1 presents a dynamic programming algorithm that can always be used to solve the preceding problem; Section 10.2.2 gives a more efficient algorithm that can be employed when all the project return functions are concave; and Section 10.2.3 analyzes the special case, known as the knapsack problem, where project investments are made by purchasing integral numbers of shares, with each project return being a linear function of the number of shares purchased. Models in which probability is a key factor are considered in Section 10.3. Section 10.3.1 is concerned with a gambling model having an unknown win probability, and Section 10.3.2 examines a sequential investment allocation model where the number of investment opportunities is a random quantity.
A Deterministic Optimization Model
Suppose that you have m dollars to invest among n projects and that investing x in project i yields a (present value) return of fi(x), i = 1, = n. The problem is to determine the integer amounts to invest in each project so as to maximize the sum of the returns.
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.