# Tagged Questions

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 concerning Lundberg-Exponent

My question is based on the beginning of Chapter 8.3.2 in the book "Modelling Extremal Events" by Embrechts,Klüppelberg and Mikosch. We consider a Cramer-Lundberg-Model and assume that the conditions ...
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### Effective Rate of Interest and Inflation Problem

I'm trying to solve the following question from a past SOA FM exam, but there are no posted solutions so I'm not sure if I'm headed in the right direction. John deposits 10, 000 in a saving ...
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### Deductible and Policy limit [closed]

I'm trying to figure out the solution to the following problem. I was working with the Adapt program for the p exam but I can't find the solution anywhere. Problem: Consider an insurance policy ...
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### Finding pdf of X+Y - Finan 42.2

I am looking through Marcel Finan's 'A Probability Course for the Actuaries' and I am stuck on problem 42.2. It is as follows: Let X be an exponential random variable with parameter $\lambda$ and ...
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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 ...
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### Evaluating differing perpetuity payments

A perpetuity pays 1900 dollars on January 1 of 1980, 1982, 1984, ..., and pays X dollars on January 1 of 1981, 1983, 1985, ... If the present value on January 1, 1975 is 26500 dollars, and the ...
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### Theory of Interest - Going from discount rate - annual effective and nominal to force of interest

[![Force of Interest & Discount Rate][1]][1] Hi there guys, I'm new to Theory of Interest and I might have started studying a bit too late, but I really need to just grasp this before the end of ...
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### Proove the approximation for risk premium

Exercise comes from Bowers' "Actuarial Mathematics". I'm self-studying and have virtually no clue how to approach it. We make no assumptions about either utility function or distribution of X. Let $w$...
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### Actuarial and Investment companies problem.

I am trying to study for the first actuarial exam, and I'm stuck with this problem. I tried to use Venn Diagrams to solve it, but I cannot reach the correct solution. The book said $135$ people have ...
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### Explicit formula for recursive sequence.

Consider the series defined by $$P_n=(P_{n-1}-a)b\ .$$ $$P_0=c$$ Basically the number sequence $P_n$ represents the current Principal balance of a debt and constants $a$ and $b$ are constants or ...
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### Clarification on a collared stock being equivalent to a bull spread?

The following is a question on financial math from the financial math actuarial exam: Earlier in the manual, the author stated that a collared stock is equivalent to a bull spread. Therefore, in ...
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### Order Statistics for IIND Variables

Given 3 exponential random variables with different means (for example 1, 2, 3), how can one calculate E(X) for MIN(X1,X2,X3)?
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### Conditional expectation of insurance payment

I'm trying to solve the following problem: An insurance policy is written to cover a loss, X, where X has a uniform distribution on (0, 1000). At what level must a deductible be set in order for the ...
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### Find the highest price which an investor can pay and still be certain of a yield of:

I'm having trouble understanding this example in Kellison's Theory of interest: Consider a 100 par value 4% bond with semiannual coupons callable at 109 on any coupon date starting 5 years after the ...
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### Having trouble solving this Exam FM problem with zero coupon bonds.

You have two 4-year annual-coupon bonds, each one of them has a face value of 8000 and a redemption value of 8000. The coupon rate of first bond is 7% and its price is 7908.57, while the second has a ...
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