Negash G. Medhin And Chuan Xu. The Role of Risk Aversion in Stochastic Differential Reinsurance Games. Neural, Parallel, and Scientific Computations 28 (2020) No.4,  223-245

https://doi.org/10.46719/npsc20202841

ABSTRACT.
In this paper, the role of risk aversion in stochastic reinsurance games is investigated.
The state of diffusion processes in reinsurance games can be fully characterized by probability density functions (PDFs). Therefore, we derive the associated PDFs by the Fokker-Planck equation (FPE). General PDFs, adapted to high dimensions and with covariance terms, are given. The Chang-Cooper scheme is extended to the high dimensions to perform numerical analysis for our problem. The scheme is validated by an example rst to show the accuracy. Then, a procedure based on the previous scheme is developed to study the relationship between the risk aversion coefficient and the expected utility of terminal wealth for reinsurance games numerically. With the procedure, we can show the trend between the two. In our case, a larger risk aversion results in higher terminal wealth. However, the benet of raising risk aversion decays significantly after certain thresholds.
For comparison, the Monte-Carlo method is also applied, and the result reveals the same pattern as before.

AMS (MOS) Subject Classification. 91A15, 37N30.