Optimal risk transfer under quantile-based risk measurers

Abstract

The classical problem of identifying the optimal risk transfer from one insurance company to multiple reinsurance companies is examined under some quantilebased risk measure criteria. We develop a new methodology via a two-stage optimisation procedure which allows us to not only recover some existing results in the literature, but also makes possible the analysis of high dimensional problems in which the insurance company diversifies its risk with multiple reinsurance counter-parties, where the insurer risk position and the premium charged by the reinsurers are functions of the underlying risk quantile. Closed form solutions are elaborated for some particular settings, although numerical methods for the second part of our procedure represent viable alternatives for the ease of implementing it in more complex scenarios. Furthermore, we discuss some approaches to obtain more robust results.

Some mathematical aspects of price optimisation

“…Very recent contributions focus on the issues of price optimisation, mainly from the ethical and regulation points of view, see [5,6]. It is important to note that optimality issues in insurance and reinsurance business, not directly related to the problems treated in this contribution, have been discussed in various context, see [7,8,9,10,11,12,13] and the references therein.…”

Optimal Reinsurance with One Insurer and Multiple Reinsurers

“…an insurer and a reinsurer, recently some progress have been made on addressing the optimal reinsurance in the presence of multiple reinsurers. See for example Asimit et al (2013), Chi and Meng (2014), and Cong and Tan (2014).…”

“…First, we allow for very general preferences of the insurer. In contrast, both Asimit et al (2013) and Cong and Tan (2014) assume that the insurer's preference is to minimize its value at risk (VaR) while Chi and Meng (2014) assume conditional value at risk (CVaR), in addition to VaR.…”

“…Second, we allow for more than two reinsurers while the optimal reinsurance models of Asimit et al (2013) and Chi and Meng (2014) explicitly assume two reinsurers. Third, both Asimit et al (2013) and Chi and Meng (2014) impose the condition that one of the reinsurers adopts the expected value premium principle.…”

“…Third, both Asimit et al (2013) and Chi and Meng (2014) impose the condition that one of the reinsurers adopts the expected value premium principle. Our proposed model, on the other hand, does not have such constraint.…”