# 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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### Proof of continuous force of interest with infinitely compounded interest rate. For actuaries, delta and i upper infinity

Specifically, we know the following: $$(1+\frac{i^{(2)}}{2})^2 =(1+\frac{i^{(4)}}{4})^4=(1+\frac{i^{(12)}}{12})^{12}= 1+i,$$ Where $i^{(2)}$, $i^{(4)}$, and $i^{(12)}$ are the interest rates ...
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### Certainty equivalent related to the net present value when there is no interest

Throughout we work with the assumption that there is no force of interest (i.e. the interest rate is $i=1$). Consider a lottery $X$ that pays $1000$ with probability $e^{-1}$ and $0$ otherwise. Then ...
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### What is the actuarial present value of a life insurance given in this question?

I need help on approaching a particular question regarding actuarial science. I just need a rough concept on how to do it, so I won't provide any extra data to keep this simple. For these questions, ...
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### Present value of varying annuities

I need help with the following questions. In order to answer these questions, I am only allowed to use two of the tables of values for $\ddot a_n , \bar a_n$ (continuous annuity) and $(I \ddot a)_n$ ...
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### Calculate the probability that a randomly chosen claim on this policy is processed in four hours or more

I'm not sure how to approach this question, can someone please help me? An insurance policy is written to cover a loss X where X has density function f(x) = (2/9)x for 0 ≤ x ≤ 3 and 0 ...
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### Recurrence relations for annuities

I need help figuring out recurrence relations for various annuities. I've attacked the questions below and my responses. I'm not too sure what the recurrence relation is for d) however. I have ...
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### accumulated value in geometric progression

In a general form, i know how to compute the PV of an annuity that follows a geometric progression. But how do i compute it when it's the accumulated value? let's say a payment of 100/ year with ...
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### Maximum likelihood estimators of the parameter of an aggregate loss (Poisson frequency, exponential loss)

Question: $$N\sim Poisson(\theta), X\sim exp(\theta)$$ $$S = X_1 + X_2 + ... + X_N$$ With $4$ observed aggregate loss $s_1, s_2, s_3, s_4$. What's the maximum likelihood estimator of $\theta$? My ...
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### Variation of $_n d_x = l_x - l_x+n$ (Actuarial notation used)

I am having trouble deriving this equation I understand that $l_x=l_0 s(x)$ $s(x) = e^{-\int_0^x \mu (u)du}$ and from there I derived $l_{x+n} = l_xe^{-\int_x^{x+n}\mu(u)du}$. I tried playing ...
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### Solving for the amount of level payments proportional to interest due from sample SOA exam

this is a problem from practice exam FM that I am studying for: A 20-year loan of 1000 is repaid with payments at the end of each year. Each of the first ten payments equals 150% of the amount of ...
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### Financial Appraisal - Discounting

Suppose we were given a discounted cost of \$50,000, which has been generated using a discount factor of 3.5% and a time-horizon of 45 years. Is it possible to obtain what the non-discounted cost is ...
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### Variable life insurance payout

How do I calculate the payout required at a given time such that my wife can replace my income with a combination of investment returns and withdrawals such that it has dwindled to zero by the end of ...
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### Financial Maths Question: How to calculate the duration of a cash flow

The question reads: A firm has liabilities as follows: £2,910 at time t = 0 and £7,501 at time t = 4 (time is measured in years). On the asset side the firm has two payments, each for £5,000, at time ...
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### Pesky Bond Pricing Question involving Redemption Yield

Consider a bond with face value £100 with semi-annual coupons at a rate 3% per annum and redeemable at par in ten years. If the bond is to produce a gross redemption yield of 3.5% per annum, what is ...