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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.

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, computer science and more.

Originally, actual science used deterministic models in the construction of tables and premiums. It has gone through revolutionary changes since the proliferation of high-speed computers and the union of stochastic actuarial models with modern financial theory.

To be used with more specific tags, such as , and . See https://en.wikipedia.org/wiki/Actuarial_science for more information.

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Why modelling Survival probabilities using the force of mortality

As an actuarial student I would like to know why the force of mortality is used to model survival probabilies. It wouldn't be easier to model directly the shape of the survival function? the force of mortality is defined…
Enzo
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Annuity-Immediate Problem with Varying Payment (ASM FM Study Manual 10th Edition, Practice Exam 2 P.679 Q1)

The question asks: 'A 35-year annuity immediate pays $1.05^{35}$ in the first year, $1.05^{34}$ in the second year, etc., until 1.05 is paid in the 35th year. The PV of this annuity at 5% effective is X. Determine X.' I understand the answer =…
Kevin
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Increasing and then level perpetuity

this is my first actuarial question so correct any mistakes I make in formatting! We have a perpetuity with annual payments. The first payment is $ \$500$ and then payments increase by $ \$25$ each year until they become level at $ \$900$. We want…
David South
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Quadratic Utility Function

Before this homework, "Calculate the corresponding premium for a quadratic utility function", we got to solve this example: Suppose the insurer has an exponential utility function with parameter $\alpha$. What is the minimum premium $P^-$ to be…
user175306
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How to calculate the yield to maturity?

I am looking at an example problem in my textbook and its solution. Can someone look at this picture/ problem and its solution and tell me where they got the yield to maturity.
Ayoshna
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Please can you help me with this proof

Prove that $\frac{1}{a_\overline{n|} } = i + \frac{1}{s_\overline{n|}}$ all at $i$ This is what I've done so far. Please feel free to change the approach entirely $$\frac{1}{a_\overline{n|}} = \frac{i}{1-v^n}$$ $$= \frac{i}{1-(1+i)^{-n}} \times…
StephanCasey
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Continuous pyments with continuous compounding

At time $t=0$ saving account balance is $0$. Then we start continuous payments with intensivity $C_t$. Continuous compounding intensivity is $\delta_t=\frac{1}{1+t}$. Accumulated value of funds at time $t$ is $t(1+t)$. Find $C_t$. I try to find…
user109447
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Present value involving deferred annuities - is this a typo?

Catfish Hunter’s 1974 baseball contract with the Oakland Athletics called for half of his 100,000 salary to be paid to a life insurance company of his choice for the purchase of a deferred annuity. More precisely, there were to be semi-monthly…
Mitchell
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Determine the probability for a pair (x, y) that:

(a) y dies after the year of death of x (b) y dies after x, assuming that times of death over the year of death are equally distributed. Tabulate and compare the results obtained for a few concrete values. I know how to calculate the probability…
lenamagdalena
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Curtate Expectation of life aged x question

Curtate Expectation of life aged x So I did @k=0, P(60)= 0.9 @k=1, P(61)= 0.9*[0.9*(1-(0.1*1)) = 0.729 @k=2, P(62)= 0.90.729 [0.9*(1-(0.1*2)) = 0.47239 Not sure if that's right, or where to go from there. Can anyone help with a detailed working for…
user22222969
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Survival Models for Actuarial , npx

I was given: $$\mathring e_x = 12.38763065, \quad \mathring e_{x+3} = 11.65757292$$ and $${}_2 q_{x+1} = 0.1201466209, \quad q_x = 0.05917676022$$ and I was asked to find: $$\require{enclose} \mathring e_{x : \enclose{actuarial}{3}}$$ I want to use…
MathStudent127
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How to prove that $\mathring{e}_x \le \mathring{e}_{x+1} + 1$ - AMLCR Exercise 2.10a

I'm going through Actuarial Mathematics for Life Contingent Risks, 3rd. ed Exercise 2.10. Part a. is the following question: Show that $\mathring{e}_x \le \mathring{e}_{x+1} + 1$. Based on the definition from the book as well as the distributional…
qxzsilver
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Survival Analysis - integrating the survival probability

recently I am doing 1 question A life aged (40) is subject to an extra risk for the next year only. Suppose the normal probability of death is 0.003, and that the extra risk may be expressed by adding the function 0.03(1-t) to the normal force of…
aukk123
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Calculating $(IA)_{50}$

Mortality of (50) follows De Moivre's law with w=100 and i=0.06. I find it hard to evaluate the value of $(IA)_{50}$. Any tip will be much appreciated
Heisenberg
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Varying payment- with both increasing and decreasing annuity

I am trying to find the present value of an annuity-immediate such that the first payment is $1000$, and each subsequent payment increases by $100$ until the payments reach $2000$, but then decreases annually by $200$ until the final payment of…
comp890
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