Financial Mathematics Archives - Infinity is Really Big

April 23, 2019April 30, 2019

Gompertz-Makeham Survival Model

Studying for Exam LTAM, Part 1.7

You susceptibility to death generally grows higher as you age. This is an unfortunate fact of life. However, life insurance can help protect your family if you should die. It is a good idea to purchase life insurance, especially if you have dependents.

So far we have explored … Read the rest

March 13, 2019March 13, 2019

New Video: Immunization, Part 7

Balancing Cashflows is Good, Prioritization of God in Life is Even Better

My newest video continues my series on financial mathematics for actuarial exam 2/fm preparation (it is Video #175 of that series). It also continues the topic of the latest videos, which is immunization of liability cashflows by asset cashflows.

Furthermore, I continue to make use of a spreadsheet … Read the rest

March 1, 2019March 1, 2019

New Video: Internal Rate of Return

Lecture 5 on Financial Mathematics for Actuarial Science

Financial Math for Actuaries, Lecture 5: Internal Rate of Return (IRR), a.k.a. Yield Rate

I have been working on developing video resources for Bethel University‘s course on Financial Mathematics for Actuarial Science for the past couple of years.

Mostly this has consisted of making many very detailed problem-solving and conceptual videos … Read the rest

February 22, 2019February 22, 2019

New Video: Immunization, Part 6

Checking Conditions for (Lack of) Redington Immunization in a Spreadsheet

Spreadsheets are extremely useful tools for many business, academic, and personal applications.

Examples of situations where spreadsheets are useful include: budgeting (totals, averages, piecharts), descriptive statistics (means, standard deviations, correlations, graphs), inferential statistics (t-statistics, p-values, ANOVA regression tables), finance (monthly payments, internal rates of return), simulation (random number generation, discrete … Read the rest

February 20, 2019February 21, 2019

New Video: Immunization, Part 5

Redington immunization is a concept that can be defined in terms of derivatives of present value functions.

Given asset cashflows $A_{0},A_{1},A_{2},\ldots,A_{n}$ and liability cashflows $L_{0},L_{1},L_{2},\ldots,L_{n},$ each set of flows occurring at times $t=0,1,2,\ldots,n,$ the expressions $P_{A}(i)=\displaystyle\sum_{t=0}^{n}A_{t}(1+i)^{-t}$ and $P_{L}(i)=\displaystyle\sum_{t=0}^{n}L_{t}(1+i)^{-t}$ represent the present values of these cashflows, as functions of an arbitrary periodic interest rate $i.$

If we let $h(i)=P_{A}(i)-P_{L}(i)=\displaystyle\sum_{t=0}^{n}C_{t}(1+i)^{-t},$ where $C_{t}=A_{t}-L_{t},$ then we say the liabilities are Redington immunized … Read the rest

February 12, 2019February 12, 2019

New Video: Immunization, Part 4

In “New Video: Immunization, Part 3“, I showed that if a liability cashflow is not immunized by an asset cashflow, we might be able to make modifications to change this state of affairs.

In particular, the time of payment of one of the asset amounts could be changed to achieve, at least, Redington immunization. To be even … Read the rest

February 4, 2019February 12, 2019

New Video: Immunization, Part 3

Immunization of a liability cashflow by an asset cashflow can help to cushion a company when interest rates change, but is it always possible?

My most recent video is “Actuarial Exam 2/FM: Liabilities Not Immunized by Assets in Spite of PV and Duration Matching” (Financial Math for Actuarial Exam 2 (FM), Video #171. October 2018 SOA Sample Exam, Problem #127). … Read the rest

February 1, 2019February 1, 2019

New Video: Immunization, Part 2

In the previous post, “New Video: Immunization, Part 1“, I introduced the idea of Redington immunization of liability cashflows by asset cashflows.

It was a post that delved into the details of my previous YouTube video “Actuarial Exam 2/FM Prep: Use Redington Immunization to Find a Ratio of Assets in a Portfolio” embedded … Read the rest

January 30, 2019January 31, 2019

New Video: Immunization, Part 1

It is very important for any business, including any insurance company, to be able to meet their financial liability obligations.

A major class of liabilities that insurance companies must plan for are the claims from their customers. For example, if a person buys car insurance, then the insurance company would be obligated to pay for, among other things, some or … Read the rest

January 24, 2019January 28, 2019

New Video: Rebalancing a Bond Portfolio for a New Macaulay Duration

Rebalancing a portfolio is an important kind of financial planning action. It can be done to increase your rate of return or to change the susceptibility of the value of your investments to changes in yield rates.

For a coupon bond, the “duration” or “length” of the bond is a way to measure its susceptibility to … Read the rest