2018/05/23 by Thai Nguyen, Nguyen, Thai, Mitja Stadje +1
Economics, Econometrics and Finance · Health Professions · Social Sciences · #49N99 #91G10 #91G80 #93E20 #FOS: Economics and business #Global Health Care Issues #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Mathematical Finance (q-fin.MF) #Portfolio Management (q-fin.PM)
paper · pdf · doi:10.48550/arxiv.1805.09068
openalex publication_date 2018/05/23 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
This paper studies a Value-at-Risk (VaR)-regulated optimal portfolio problem\nof the equity holders of a participating life insurance contract. In a setting\nwith unhedgeable mortality risk and complete financial market, the optimal\nsolution is given explicitly for contracts with mortality risk using a\nmartingale approach for constrained non-concave optimization problems. We show\nthat regulatory VaR constraints for participating insurance contracts lead to\nmore prudent investment than in the case of no regulation. This result is\ncontrary to the situation where the insurer maximizes the utility of the total\nwealth of the company (without distinguishing between contributions of equity\nholders and policyholders), in which case a VaR constraint may induce the\ninsurer to take excessive risks leading to higher losses than in the case of no\nregulation. Compared to the unregulated problem, the VaR-constrained strategy\nleads to a higher expected utility for the policyholders, highlighting the\npotential usefulness of a VaR-regulation in the context of insurance. The\nprudent investment behavior is more significant if a VaR-type regulation is\nreplaced by a portfolio insurance (PI)-type regulation. Furthermore, a stricter\nregulation (a smaller allowed default probability in the VaR problem or a\nhigher minimum guarantee level in the PI problem) enhances the benefit of the\npolicyholder but deteriorates that of the insurer. For both types of\nregulation, the gains in terms of expected utility are greater for higher\nparticipation rates, while being smaller for higher bonus rates. We also extend\nour analysis to frameworks where dividend and premature death benefit payments\nare made at an intermediate time date.\n