A finite-horizon insurance model is studied where the risk/reserveprocess can be controlled by reinsurance and investment in thefinancial market. Our setting is innovative in the sense that wedescribe in a unified way the timing of the events, that is, thearrivals of claims and the changes of the prices in the financialmarket, by means of a continuous-time semi-Markov process which appearsto be more realistic than, say, classical diffusion-based models.Obtaining explicit optimal solutions for the minimizing ruinprobability is a difficult task. Therefore we derive a specificmethodology, based on recursive relations for the ruin probability, toobtain a reinsurance and investment policy that minimizes anexponential bound (Lundberg-type bound) on the ruin probability.
"Ruin probabilities in a finite-horizon risk model with investmentand reinsurance." J. Appl. Probab. 49 (4) 954 - 966, December 2012. https://doi.org/10.1239/jap/1354716650