From the point of view of the first insurer, we determine the ideal proportion of an insurance policy, in a Levy market, to be re insured and the expected value attained using Stochastic control (Dynamic programming). A Levy process is used to model the reserves of the insurer given that a re insurance policy has been implemented as a means of risk transfer. For completeness, the results are analytically and graphically compared with those of a diffusion model with the aid of Matlab. Financial mathematicians, actuaries, and insurers would find this book useful. A background in stochastic differential equations will make understanding easier.