Proof of explicit expression for ruin probability
I'm trying to derive a proof for the probability of ruin in continuous time which is given by the expression
$$
psi(u)=frac{1}{1+theta}mathrm{e}^{-frac{alphatheta}{1+theta}u}
$$
This expression is given under the assumption that claim amounts are exponentially distributed with $X_isim mathrm{Exp}(alpha)$ and the premium income per unit of time is $(1+theta)lambda Bbb E(X)$
I don't understand how to derive the expression in the picture.
finance
edited 2 days ago
alexjo
12.3k1329
asked Dec 24 '18 at 14:25
Sobia
32
add a comment |
I'm trying to derive a proof for the probability of ruin in continuous time which is given by the expression
$$
psi(u)=frac{1}{1+theta}mathrm{e}^{-frac{alphatheta}{1+theta}u}
$$
This expression is given under the assumption that claim amounts are exponentially distributed with $X_isim mathrm{Exp}(alpha)$ and the premium income per unit of time is $(1+theta)lambda Bbb E(X)$
I don't understand how to derive the expression in the picture.
finance
edited 2 days ago
alexjo
12.3k1329
asked Dec 24 '18 at 14:25
Sobia
32
Please give more details. Where do you start from?
– alexjo
2 days ago
add a comment |
I'm trying to derive a proof for the probability of ruin in continuous time which is given by the expression
$$
psi(u)=frac{1}{1+theta}mathrm{e}^{-frac{alphatheta}{1+theta}u}
$$
This expression is given under the assumption that claim amounts are exponentially distributed with $X_isim mathrm{Exp}(alpha)$ and the premium income per unit of time is $(1+theta)lambda Bbb E(X)$
I don't understand how to derive the expression in the picture.
finance
edited 2 days ago
alexjo
12.3k1329
asked Dec 24 '18 at 14:25
Sobia
32
I'm trying to derive a proof for the probability of ruin in continuous time which is given by the expression
$$
psi(u)=frac{1}{1+theta}mathrm{e}^{-frac{alphatheta}{1+theta}u}
$$
This expression is given under the assumption that claim amounts are exponentially distributed with $X_isim mathrm{Exp}(alpha)$ and the premium income per unit of time is $(1+theta)lambda Bbb E(X)$
I don't understand how to derive the expression in the picture.
finance
finance
edited 2 days ago
alexjo
12.3k1329
asked Dec 24 '18 at 14:25
Sobia
32
edited 2 days ago
alexjo
12.3k1329
asked Dec 24 '18 at 14:25
Sobia
32
edited 2 days ago
alexjo
12.3k1329
edited 2 days ago
alexjo
12.3k1329
edited 2 days ago
alexjo
12.3k1329
12.3k1329
asked Dec 24 '18 at 14:25
Sobia
32
asked Dec 24 '18 at 14:25
Sobia
32
asked Dec 24 '18 at 14:25
Sobia
32
32
Please give more details. Where do you start from?
– alexjo
2 days ago
add a comment |
Please give more details. Where do you start from?
– alexjo
2 days ago
Please give more details. Where do you start from?
– alexjo
2 days ago
Please give more details. Where do you start from?
– alexjo
2 days ago
add a comment |
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Please give more details. Where do you start from?
– alexjo
2 days ago