A health insurance pricing model based on prevalence rates: Application to critical illness insurance

The Italian health insurance market is currently undersized. The paucity of assured data and the discontinuous statistical surveys carried out by the National Institute of Statistics (ISTAT) represent one of the main obstacles to the insurance market development. The paper sets forth a parametric model to estimate technical basis for health insurance policies when data are limited and only aggregated information on mortality and morbidity is available. The probabilistic framework is based on a multiple state continuous and time inhomogeneous Markov model. We provide an estimate of transition intensities from the healthy state to the sickness state when only prevalence rates of sickness are available, according to an extension and modification of the methodology proposed in Olivieri (1996) for Long Term Care insurance. We assume that mortality intensity of both healthy and sick lives is modelled by two independent Gompertz–Makeham models.     

Optimal investment of DC pension plan under short-selling constraints and portfolio insurance

In this paper we investigate an optimal investment problem under short-selling and portfolio insurance constraints faced by a defined contribution pension fund manager who is loss averse. The financial market consists of a cash bond, an indexed bond and a stock. The manager aims to maximize the expected S-shaped utility of the terminal wealth exceeding a minimum guarantee. We apply the dual control method to solve the problem and derive the representations of the optimal wealth process and trading strategies in terms of the dual controlled process and the dual value function. We also perform some numerical tests and show how the S-shaped utility, the short-selling constraints and the portfolio insurance impact the optimal terminal wealth.     

Valuation and risk assessment of participating life insurance in the presence of credit risk

In participating life insurance, management decisions regarding the asset composition can substantially impact the value of a policy from the policyholders’ perspective as well as the insurer’s risk situation. Due to the long-term guarantees often embedded in these contracts, life insurers typically invest a considerable portion of their capital in long-term assets such as corporate and government bonds. Besides interest rate risk, the value of these bond investments is thus particularly influenced by credit risk. Thus, the aim of this paper is to examine the impact of market risk associated with the asset composition on fair valuation and risk assessment with focus on credit risk and its interaction with equity risk and interest rate risk. Our analysis emphasizes that the consideration of credit risk associated with bonds has a strong impact on the fair valuation and risk measurement in the context of participating life insurance contracts, even in case of higher grade bond exposures.     

On the management of life insurance company risk by strategic choice of product mix,investment strategy and surplus appropriation schemes

The aim of this paper is to analyze the impact of management’s strategic choice of asset and liability composition in life insurance on shortfall risk and the shareholders’ fair risk charge. In contrast to previous work, we focus on the effectiveness of management decisions regarding the product mix and the riskiness of the asset side under different surplus appropriation schemes. We propose a model setting that comprises temporary life annuities and endowment insurance contracts. Our numerical results show that the effectiveness of management decisions in regard to risk reduction strongly depends on the surplus appropriation scheme offered to the customer and their impact on guaranteed benefit payments, which thus presents an important control variable for the insurer.     

Prevention efforts,insurance demand and price incentives under coherent risk measures

This paper studies an equilibrium model between an insurance buyer and an insurance seller, where both parties’ risk preferences are given by convex risk measures. The interaction is modeled through a Stackelberg type game, where the insurance seller plays first by offering prices, in the form of safety loadings. Then the insurance buyer chooses his optimal proportional insurance share and his optimal prevention effort in order to minimize his risk measure. The loss distribution is given by a family of stochastically ordered probability measures, indexed by the prevention effort. We give special attention to the problems of self-insurance and self-protection, and show that if the buyer’s risk measure decreases faster in effort than his expected loss, optimal effort is non-decreasing in the safety loading with a potential discontinuity when optimal coverage switches from full to zero. On the contrary, if the decrease of the buyer’s risk measure is slower than the expected loss, optimal effort may or may not be non-decreasing in the safety loading. In case of Pareto distributed losses, the seller sets the highest possible price under which the buyer still prefers full insurance over no insurance. We also analyze the case of discrete distributions: on the one hand, for self-protection, under the assumption that the marginal impact of the effort is higher on small losses than it is on catastrophic losses, the optimal effort is non-decreasing in the safety loading. On the other hand, in the case of self-protection, more conditions are needed, in particular, we obtain sufficient conditions for the optimal effort to be non-decreasing or non-monotone in the safety loading.