Discrete-time optimization problems in insurance with final distribution constraint

We study a few optimization problems for an insurance company who additionally aims to reach a surplus with a given target distribution at a fixed time T. First, we consider a dividends problem where dividends are distributed at deterministic dates, and we model the surplus via a diffusion process. In this setting we investigate strategies that allow either to maximise the dividends or to minimize the ruin probability, and lead to a specific distribution of the surplus at a future date. The constraint on the distribution makes the problem non-standard and has important implications in terms of risk management. Second, we consider an insurance company who targets to buy a reinsurance contract for a pool of insured, with a surplus modelled as an arithmetic Brownian motion. To achieve a certain level of sustainability (i.e. the collected premia should be sufficient to buy reinsurance and to pay the occurring claims) the initial capital is set to be zero. We only allow for piecewise constant reinsurance strategies producing a normally distributed terminal surplus, whose mean and variance lead 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)

Personal page: https://sites.google.com/site/katiacolaneri/
Link Zoom: https://univr.zoom.us/j/86803688017