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Insurers do use derivative pricing models such as Black-Scholes to price the sort of guarantees you describe. As far as I know, this used to be known as the "replication method" in the industry jargon, and it allows insurers to price guarantees in a market-consistent manner, hence enabling them to efficiently hedge them with traded instruments. In particular,...

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I dont know if i am qualified to answer this. I was an actuarial student as well. Graduated last year, but I didnt undertake further professional exams. I passed the first three exams and earned all the exemptions (3 i think) under SOA exams during my school years. I am fascinated by quantitative finance during my studies too and decided it'd be best that ...

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I will show you two different treatments, the first from the classic utility theory and the other from financial economics. Consider a risk averse market operating on a concave, monotonic and increasing utility function. Under some regularity (Von-Neumann) conditions, this is without loss of generality. Such a utility function, is unique upto a linear ...

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Assuming the annuity pays K every year from year 1 to n, you can write it’s PV as follows: $PV=K \left( \frac{1}{1+r} +\frac{1}{(1+r)^2 }+ \dots + \frac{1}{(1+r)^n} \right)$ And FV, by noting that the first K is invested for n-1 periods, and the last one is received at n: $FV=K \left( (1+r)^{n-1} + (1+r)^{n-2}+ \dots+ 1 \right)$ Now one just needs to ...

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