Some Optimisation Problems in Insurance with a Terminal Distribution Constraint

Abstract

We study two optimisation settings for an insurance company, under the constraint that the terminal surplus at a deterministic and finite time T follows a certain target distribution. 
First, we allow the insurance company to pay dividends and seek to maximise the expected discounted dividend payments or to minimise the ruin probability under the terminal distribution constraint that the surplus is Gaussian with given mean and variance. Here, we find explicit expressions for the optimal strategies in both cases, when the dividend strategy is updated at discrete points in time and continuously in time.
Second, we let the insurance company buy a reinsurance contract for a pool of insured or a branch of business. In this setting we only allow for piecewise constant reinsurance strategies producing a normally distributed terminal surplus, whose mean and variance lead, e.g. to a given Value-at-Risk at some confidence level alpha. We investigate the question which admissible reinsurance strategy produces a smaller ruin probability, if the ruin-checks are due at discrete deterministic points in time. 

This presentation is based on an joint work with Julia Eisenberg (TU Vienna) and Benedetta Salterini (Univ. of Firenze)