Figure 6

The free boundary when \(\pmb{c(1-\gamma)-rP>0}\) with different volatility. Plot of the optimal bankruptcy boundary \(h(\tau)\) as the function of time τ when \(c(1-\gamma)-rP> 0\). The parameter values used in the calculations are \(T=1\), \(N=2{,}000\), \(r=0.03\), \(\beta=0.02\), \(c=0.04\), \(\delta=0.01\), \(\gamma=0.2\), \(P=0.07\); \(h1(\tau)\) and \(h2(\tau)\) are the free boundaries when \(\sigma_{1}=0.3\) and \(\sigma_{2}=0.7\), respectively. The numerical result (see Figure 6) shows that the optimal bankrupt boundary \(h(\tau)\) is not monotonic with τ, which coincides with Theorem 5.2, at the same time, the numerical result also reveals the bankruptcy boundary \(h(\tau)\) is decreasing with respect to volatility σ.