Figure 9

The free boundary when \(\pmb{c(1-\gamma)-rP\leq0}\) with different aggregate payout ratio. Plot of the optimal bankruptcy boundary \(h(\tau)\) as the function of time τ when \(c(1-\gamma )-rP\leq0\). The parameter values used in the calculations are \(T=4\), \(N=2{,}500\), \(\sigma=0.3\), \(r=0.3\), \(\beta=0.2\), \(c=0.3\), \(\gamma=0.2\), \(P=6\); \(h1(\tau)\) and \(h2(\tau)\) are the free boundaries when \(\delta _{1}=0.15\) and \(\delta_{2}=0.2\), respectively. The numerical result (see Figure 9) shows that the optimal bankruptcy boundary \(h(\tau )\) is decreasing not only with τ, which coincides with Theorem 4.1, but also with aggregate payout ratio δ.