Some optimisation problems in insurance with a terminal distribution constraint

In this paper, we study two optimisation settings for an insurance company, under the constraint that terminal surplus at a deterministic and finite time T follows normal distribution with given mean variance. both cases, of company is assumed to follow Brownian motion drift. First, allow pay dividends seek maximise expected discounted dividend payments or minimise ruin probability constraint. Here, find explicit expressions optimal strategies in when strategy updated discrete points continuously time. Second, let buy reinsurance contract pool insured branch business. We set initial capital zero order verify whether premia are sufficient manage risk incoming claims such way desired characteristics achieved some without external help (represented, instance, by positive capital). only piecewise constant producing normally distributed surplus, whose variance lead Value Risk Expected Shortfall confidence level α. investigate question which admissible produces smaller probability, if ruin-checks due