Alarm system for insurance companies: a strategy for capital allocation

Abstract

One possible way of risk management for an insurance company is to develop an early and appropriate alarm system before the possible ruin. The ruin is defined through the status of the aggregate risk process, which in turn is determined by premium accumulation as well as claim settlement outgo for the insurance company. The main purpose of this work is to design an effective alarm system, i.e. to define alarm times and to recommend augmentation of capital of suitable magnitude at those points to reduce the chance of ruin. To draw a fair measure of effectiveness of alarm system, comparison is drawn between an alarm system, with capital being added at the sound of every alarm, and the corresponding system without any alarm, but an equivalently higher initial capital. Analytical results are obtained in general setup and this is backed up by simulated performances with various types of loss severity distributions. This provides a strategy for suitably spreading out the capital and yet addressing survivability concerns at factory level. An insurance company is required to keep capital for claim settlement. This work proposes a structure for alarm system based on modeled claim pattern that would facilitate starting with smaller initial capital and appropriately augmenting it at suitable ‘alarm’ times. ? Such alarm system naturally provides investment flexibility to investors in insurance firms. ? The work shows empirically as well as through theoretical bounds computed that the alarm system may be more effective in terms of reducing chance of ruin under certain interest regimes and for a fixed initial capital.