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This question is a part of an larger question in actuarial mathematics. It is a model of an insurance firm with periodic stochastic outflows of $X_i$, an initial wealth of u and some income paid periodically c. Then we told a specific form of the probability of not being ruined and told to find it explicitly.

The math i hope is:

Let $(X_i)_{i\geq0}$ be iid with $P(X_1=0)=1-p$ and $P(X_1=2)=p$ (the stochastic claims), $S_n=\sum _{i =0}^n X_i$ (sum of outflows), $c$ be some constant (the periodic income) and $u$ some large constant (initial wealth). I would like to show that $P(\forall n: S_n \leq n\cdot c+u)$ (probability of not being ruined) is on the form $1-ab^u$ and determine a and b.

I've realized I'm probably supposed to look at the complement and somehow use $X_i$ is almost binomial, but I can't seem to get anywhere.

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You can add the actuarial-science tag then. – Graphth Dec 18 '12 at 16:00
Done! I just reckoned it wasn't really used - so I tried to make it "just a probablity" question. – Henrik Dec 18 '12 at 16:04
I just created the tag a month or so ago. It will be used more and more as time goes on. This way, any one interested in probability or actuarial science will see it. – Graphth Dec 18 '12 at 18:23

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