Minimum capital requirement and portfolio allocation for non-life insurance: a semiparametric model with Conditional Value-at-Risk (CVaR) constraint

Abstract We present an optimization problem to determine the minimum capital requirement for a non-life insurance company. The imposes non-positive Conditional Value-at-Risk (CVaR) of insurer’s net loss and portfolio performance constraint. When expressing in semiparametric form, we demonstrate its convexity any integrable random variable representing liability. Furthermore, prove that function defining CVaR constraint formulation is continuously differentiable when liability has continuous distribution. use Kelley-Cheney-Goldstein algorithm solve form show convergence. An empirical analysis carried out by assuming three different distributions: lognormal distribution, gamma mixture Erlang distributions with common scale parameter. numerical experiments choice distribution plays crucial role since marked differences emerge comparing other two distributions. In particular, describes better right tail liabilities respect implies higher requirements assets optimal portfolios.