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Dear participants, I welcome you all to the module of Actuarial Mathematics. The aim of this module is to provide a grounding in the mathematical techniques that are of particular relevance to actuarial work in non-life insurance, life insurance and the principles of modeling which can be used to model and value known cash-flows as well as those which are dependent on death, survival, or other uncertain risks. In addition, the module will cover three main units, namely financial mathematics; life insurance mathematics, and actuarial models.
Learning Outcomes.
At the end of this module, you will be able to:
1. Apply the appropriate mathematics to answer problems pertaining to finance, life, and non-life insurance;
2. Understand the mathematics involved in managing cash flows, life, and non-life insurance contracts;
3. Apply mathematics to explore and analyze cash flows;
4. Apply the basic techniques of actuarial mathematics and its application to insurance, pensions, banking etc.
Significant features of the module:
1. This module will be taught to the second-year students in the department of Applied Statistics of the undergraduate program.
2. It gives a grounding knowledge in actuarial mathematics, especially in financial mathematics.
3. It will be taught in a blended learning mode of delivery.
4. It will equip students with a concise knowledge of actuarial mathematics.
Module developer(s):Roger Muremyi (Leader).
Email: muremyiroger@gmail.com
Phone: +250788793493
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▶Actuarial mathematics: Financial
▶ Actuarial mathematics: Life
▶ Actuarial mathematics: General -
The aim of this unit is to introduce the fundamental concepts of financial mathematics, and how those concepts are applied in calculating present and accumulated values for various streams of cash flows.
It is designed to cover:
1. The key concept of the interest rates;
2. Understand the mathematics underlying the theory of interest rate, especially simple and compound interest rates.
Learning Outcomes:At the end of this unit, participants will be able to:
1. Understand the basics of financial mathematics pertaining to interest rates.;
2. Given any two of interest rate, present value, or future value, calculate the third based on simple or compound interest.;
3. Write the equation of value given a set of cash flows and an interest rate.
You will be engaged in different activities such as forum discussion, practical activities, and assignments as designed in different corresponding activities.-
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E-tivity 1.1 Chat
The aim of this e-tivity 1.1 is to provide essential knowledge of interest rates and calculate the cash flows involved.
From the teams of 3 students each proposed by your lecturers, do the following:
Read the following resources:
• “Lecture notes on financial mathematics”
Task:
1. Join his/her respective group discussion about 90 minutes
2. Make a brief presentable note to post in the discussion by:
(i) Key terms/verbs used in financial mathematics pertaining to the simple interest rate;
(ii)Describe the basic terms characterizing the interest rate.
3. Post your work in the discussion forums by Wednesday at 23h30.
4. Read what other students posted on your team and comment on at least three work of your team.
5. Send the final work to your e-moderator for assessment and send feedback by Friday at 23h00 in the week this unit is taught. -
Assignment(e-tivity 1.2)
This e-tivity 1.2 is designed as an assignment to be submitted helps well prepare you to understand the basics of the interest rate.
Read the following resources:
• “Deterministic Cash-Flows” available at http://www.columbia.edu/~mh2078/FoundationsFE/DeterministicCashFlows.pdf
• Lecture notes/slides
Task:
Find how long should be left $1000 to accumulate at 6% effective in order it will amount to twice the accumulated value of another $1000 deposited at the same time at 4% effective.
Send the file of your summary to e-moderator electronic mail(nhategekimana@ur.ac.rw) before the start of a new unit, exactly by Tuesday at 23h00 in the week this unit is taught. -
E-tivity 1.3 Forum
This e-tivity 1.3 helps well prepare you to understand the equations governing the cash flows for a given financial transaction.
Read the following resources:
• “Stephen G. Kellison (2009). The Theory of Interest, 3rd Edition. McGraw-Hill."
• Lecture notes
Task:
1. Read chapter 11, pages 1-39, and then
2. Let’s take an ideal investment of amount S that would accumulate cashflows at the nth period. Determine the sequence of the interest rate up to the last period.
3. What is the relationship between the present value and the future value of cash flows?
4. Post the file of your summary in the discussion board of this unit and wait for feedback from the e-Moderator. -
E-tivity10 Forum
Show your performance.
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Students mustMark as done
Match the following types of insurance products with their descriptions
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Aim of the unit: This unit aims- to provides a short introduction to financial markets mostly capital markets and asset pricing, notably interest rates models.
Intended learning outcomes:
At the end of this unit, you will be able to:
1. Describe the important differences between the stock, bond, and derivative securities.;
2. Critically evaluate the evidence for informational efficiency of stock markets;
3. Explain how to value a bond by using present value.-
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E-tivity 2.1 Forum
The aim of this e-tivity is to provide essential knowledge and a short introduction to stock markets.
From your respective groups, do the following:
Read the following resources:
• “Lecture notes/slides”
• “Stock market terms and definitions” available at https://www.cma.rw/index.php?id=81”
Task:
1. Join his/her respective group discussion about 90 minutes
2. Describe the components of the stock market and conceptualize them for the Rwanda capital market.
3. Post your work in the discussion forums by Wednesday at 23h30.
4. Read what other students posted in your team and comment on at least two work of your team.
5. Send the final work to your e-moderator for assessment and send feedback by Friday at 23h00 in the week this unit is taught. -
E-tivity 2.2 Forum
This e-tivity 2.2 is to provide the essential knowledge on the efficient market.
From your respective groups, do the following:
Read the following resources:
• “Lecture notes/slides”
• “Richard B., et al (2020). Efficient Markets and Behavioral Finance. Principles of Corporate Finance(pp,338-359). McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121.”
Task:
1. Join his/her respective group discussion about 90 minutes
2. How is the stock market efficient?
3. Post your work in the discussion forums by Wednesday at 23h30.
4. Read what other students posted in your team and comment on at least two work of your team.
5. Send the final work to your e-moderator for assessment and send feedback by Friday at 23h00 in the week this unit is taught. -
Assignment Two(E-tivity 2.3)
This e-tivity 2.3 is designed as an assignment to be submitted helps well prepare you to understand the basics of bond valuation.
Read the following resources:
• “Bond Valuation Overview” available at https://einvestingforbeginners.com/bond-valuation-daah/"
• Lecture notes/slides
Task:
1. Describe the regulations and valuation of bond markets in Rwanda.
2. Send the file of your summary to the e-moderator electronic mail(nhategekimana@ur.ac.rw) before the start of a new unit, exactly by Friday at 23h00 in the week this unit is taught.
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This chapter introduces a solid grounding in the subject of a single life insurance, and the analysis of life assurance and life annuities, including pension contracts and as well mathematical methods for managing the risk in life insurance. A detailed monographs on this chapter can be found in
Gerber.U & Samuel H.Cox(1995). Life Insurance Mathematics, second edition. Swiss Association of Actuaries Zurich
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