Find the maximum expected holdings, Mathematics

Assignment Help:

Problem:

A person has 3 units of money available for investment in a business opportunity that matures in 1 year. The opportunity is risky in that the return is either double or nothing. Based on past performance, the likelihood of doubling one's money is 0.6, while the chance of losing an investment is 0.4. Money earned one year can be reinvested in a later year and investments are restricted to unit amounts.

When dynamic programming is used to find the investment strategy for the next 4 years that will maximize the expected total holdings at the end of that period, the problem is formulated as a four-stage process with each stage representing a year. The states sj are the amounts of money available for investment for stage j (j = 1; 2; 3; 4).

Let fj(sj) denote the maximum expected holdings at the end of the process, starting in state sj at stage j.

(a) By clearly explaining your reasoning show that a recursive formula for finding the maximum expected holdings at the end of four years is given by

2018_Find the maximum expected holdings at the end of the four years.png

for j = 1; 2; 3 and 4, where the values of α and β are to be determined.

(b) Write down an expression for f5(s).

(c) Find the maximum expected holdings at the end of the four years.


Related Discussions:- Find the maximum expected holdings

Math on a spot, compare: 643,251: 633,512: 633,893. The answer is 633,512.

compare: 643,251: 633,512: 633,893. The answer is 633,512.

Total linear attenuation, Consider the task of identifying a 1 cm thick bre...

Consider the task of identifying a 1 cm thick breast cancer that is embedded inside a 4.2 cm thick fibroglandular breast as depicted in Fig. The cancerous tumor has a cross

Define combined functions, Q. Define Combined Functions? Ans. We a...

Q. Define Combined Functions? Ans. We are often interested in functions which combine a trigonometric function with another type of function.  For example, y = x + sinx wi

Mathematical science, state tha different types of models used in operation...

state tha different types of models used in operations research.

Determine the conditional probability, Consider a class of 55 students. The...

Consider a class of 55 students. The student names are placed in a hat and 3 names are randomly drawn without replacement. a) If the first person drawn was named the class presi

Can religious wars be avoided in the future, To what extent do you think re...

To what extent do you think religious beliefs should justify war? How is this shown in "The Song of Roland"? Cite examples of how religious beliefs have led to war in the last two

Summation notation, SUMMATION NOTATION Under this section we require to...

SUMMATION NOTATION Under this section we require to do a brief review of summation notation or sigma notation.  We will start out with two integers, n and m, along with n a

Differentiate quotient rule functions, Example of quotient rule : Let's no...

Example of quotient rule : Let's now see example on quotient rule.  In this, unlike the product rule examples, some of these functions will require the quotient rule to get the de

Properties of integer exponents, Note that there are two possible forms for...

Note that there are two possible forms for the third property. Usually which form you use is based upon the form you want the answer to be in. Note as well that several of these

how large a sample is necessary to have a standard error, If the populatio...

If the population standard deviation is o=8, how large a sample is necessary to have a standard error that is: a.  less than 4 points? b.  less than 2 points? c.  less than 1 poin

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd