Asset liability management for an ordinary insurance system with proportional reinsurance in a CIR stochastic interest rate and Heston stochastic volatility framework

Figure 1.  Evolutions of the CIR stochastic interest rate $r(t)$ and Heston stochastic volatility $\sigma(t)$ within the investment horizon $[0,\ T]$

Figure 2.  Evolutions of the risky assets' prices for the insurer and the reinsurer

Figure 3.  Evolutions of the wealth processes for the insurer and the reinsurer

Figure 4.  The dynamic behaviour of (a) the optimal reinsurance control strategy $\psi^{*}(t)$, (b) the optimal investment strategy for the insurer $\pi^{*}(t)$ and (c) the optimal investment strategy for the reinsurer $u^{*}(t)$

Figure 5.  Sensitivities of $\psi^{*}(t)$ with respect to $\zeta(t)$

Figure 6.  Sensitivities of $\psi^{*}(t)$ with respect to $\gamma$

Figure 7.  Sensitivities of $\pi^{*}(t)$ with respect to $\gamma$

Figure 8.  Sensitivities of $\pi^{*}(t)$ with respect to the parameter $\nu$

Figure 9.  Sensitivities of the optimal investment strategy $u^{*}(t)$ for the reinsurer with respect to the interest rate $\mu$

Figure 10.  Sensitivities of the optimal investment strategy $u^{*}(t)$ for the reinsurer with respect to the risk aversion coefficient $q$

Figure 11.  Sensitivities of the optimal investment strategy $u^{*}(t)$ for the reinsurer with respect to the positive correlation coefficient

Figure 12.  Sensitivities of the optimal investment strategy $u^{*}(t)$ for the reinsurer with respect to the negative correlation coefficient.

Figure 13.  Sensitivities of the optimal investment strategy $u^{*}(t)$ for the reinsurer with respect to the mean reversion speed $\kappa$ when $q = 4$ and $\rho>0$

Figure 14.  Sensitivities of the optimal investment strategy $u^{*}(t)$ for the reinsurer with respect to the mean reversion speed $\kappa$ when $q = 2$ and $\rho <0$

Figure 15.  Sensitivities of the optimal investment strategy $u^{*}(t)$ for the reinsurer with respect to "volatility of volatility" $\xi$ when $q = 2$ and $\rho <0$

Figure 16.  Sensitivities of the optimal investment strategy $u^{*}(t)$ for the reinsurer with respect to "volatility of volatility" $\xi$ when $q = 2$ and $\rho>0$

Figure 17.  Sensitivities of the optimal investment strategy $u^{*}(t)$ for the reinsurer with respect to $a$

Figure 18.  Sensitivities of the optimal investment strategy $u^{*}(t)$ for the reinsurer with respect to $b$