Questions tagged [actuarial-science]

Actuarial science is a discipline that uses mathematics and statistics to assess risk. The mathematics involved in actuarial science includes probability, statistics, finance, life insurance mathematics, and more.

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Question about the mean excess loss function.

I'm new to this risk thing. I am trying to obtain the mean excess loss function evaluated at a point for the following Pareto distribution: $F(x)=1-(\frac{\theta}{x})^{\alpha}$ The excess loss ...
• 322
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Find expressions for the single sums $X$ with simple annuities

Find expressions for the single sums $X$ equivalent to the set of seven payments of Fig. 5-21 at times $(a)1,(b)5,(c)12$ and $(d)12$, assuming a rate $i$ per period. Solution: $(a)$ At $1$, $X$ is ...
• 441
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Calculate discounted cash flows for a fixed net present value with some restrictions

I was wondering what my maximal investment in year zero can be, given certain ratio that is pre-specified between cash flows, for a fixed net present value: This solution was offered by Bob: If you ...
• 335
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expected value of geometric distribution

The following question has me extremely confused: At a certain university, registrations for courses have to be made over the telephone. There are so many calls that $90$% of the time you will get a ...
• 131
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Negative Binomial and Geometric Distributions

So this is the problem I'm dealing with. An actuary has determined that the number of claims per month can take any number 0, 1, 2, 3,... and follows a negative binomial distribution with mean 3 and ...
• 131
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Redington immunization with a bond

A company pays two liabilities: $100$ in $2$ years and $50$ in $4$ years. The company is attempting to protect itself through immunization by purchasing a $3$-year, par-valued bond with annual coupons,...
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Annuity & Perpetuity problem

Suppose Joe has been paying $600$ from his monthly salary at the end of every month for the past $n$ years. After $n$ years of payments, he retires having purchased a perpetuity-due plan that begins ...
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Accumulated Value of Two investments

Suppose the force of interest is: $$F(t) = \frac{0.02 + 0.01t}{1 + 0.02t + 0.005t^2}$$ , where $t$ is the number of years beginning March 31, 2001. An investment of $100$ is made on March 31, 2002, ...
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Approximating effective interest rate on a bond

If you have a bond with the following properties: Issued at price $X$; Redeemed at price $Y$; Has a coupon rate of $p$ ; Has a term of $n$ years; then I am told, in my accounting studies, that the ...
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1 vote
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Calculating the present value of bond when face value is not equal to value at maturity

I need to calculate PV of the following bond: Face value is $1000$. It pays $50$ every $6$ months. Annual rate is $8\%$. Value at maturity is $1050$. The bond lasts $20$ years. I know how to ...
• 460
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Difference between yield rate and interest rate (solution verification)

An insurer enters into a four-year contract today. The contract requires the insured to deposit $500$ into a fund that earns an annual effective rate of $5.0\%$, and from which all claims will be paid....
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1 vote
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Bonds, Exact Matching Payments, Bank Payments

A bank accepts a 20,000 deposit from a customer on which it guarantees to pay an annual effective interest rate of 10% for two years. The customer needs to withdraw half of the accumulated value at ...
• 1,732
1 vote
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Finding the present value of a continuously varying perpertuity

A perpetuity provides for continuous payments. The annual rate of payment at time $t$ is $1$ if $0\le t<10$ and $(1.03)^{t-10}$ if $t\ge 10$. Using an annual effective interest rate of $6\%$, the ...
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Modified and Macaulay Duration

Repost but with a proposed solution.* I am practicing for an upcoming examination and came across the following problem: You are given the following information about an asset: (1) The present value ...
Suppose you were given the following information about the prices of zero-bond coupons, all with a maturity of $1$: The price of a $1$ year zero-coupon bond is $0.943$. The price of a $2$ year zero-...