This talk first consider the problem of computing different types of finite time survival probabilities for a Markov-Modulated risk model and a Markov-Modulated risk model with reinsurance, both with varying premium rates. We use the multinomial approximation scheme to derive an efficient recursive algorithm to compute finite time survival probabilities and finite time draw-down survival probabilities. Numerical results shows that by comparing with MCMC approximation, discretize approximation and diffusion approximation methods, the proposed scheme performs accurate results in all the considered cases and with better computation efficiency. Then this talk gives a new approximation method to get the optimal retention for a combination of quota-share and excess of loss reinsurance, also assuming that the insurer has partial information of the individual claim size.We then derive the optimal retention for the reinsurance arrangement by minimizing the approximated ruin probability. Some numerical examples are given which show that the proposed Bowers Gamma with Pade approximation performance better than translated gamma with De Vylder approximation. We also extend this numerical result to a risk model with prevention.