Table 1 The optimal premium and reinsurance strategies
From: A Stackelberg reinsurance-investment game with derivatives trading
Cases | \(p^{\ast}(t)\) | \(q^{\ast}(t)\) |
|---|---|---|
\((1)~N^{\theta _{F}}(t)\geq 1\) | \(\forall p\in [c_{F},\bar{c}]\) | 1 |
\((2)~N^{\bar{\theta }}(t)\leq K\) | c̄ | \(\frac{1}{1+k_{1}}(N^{\bar{\theta }}(t)+k_{1})\) |
\((3)~K\leq N^{\theta _{F}}(t)<1\) | \(c_{F}\) | \(\frac{1}{1+k_{1}}(N^{\theta _{F}}(t)+k_{1})\) |
\((4)~N^{\theta _{F}}(t)< K< N^{\bar{\theta }}(t)\) | \(a+K\gamma _{F}\sigma _{F}^{2}\varphi ^{L}(t)\) | \(\frac{1}{1+k_{1}}(K+k_{1})\) |