Dynamic pricing of general insurance in a competitive market

A model for general insurance pricing is developed which represents a stochastic generalisation of the discrete model proposed by Taylor (1986). This model determines the insurance premium based both on the breakeven premium and the competing premiums offered by the rest of the insurance market. The optimal premium is determined using stochastic optimal control theory for two objective functions in order to examine how the optimal premium strategy changes with the insurer’s objective. Each of these problems can be formulated in terms of a multi-dimensional Bellman equation. In the first problem the optimal insurance premium is calculated when the insurer maximises its expected terminal wealth. In the second, the premium is found if the insurer maximises the expected total discounted utility of wealth where the utility function is nonlinear in the wealth. The solution to both these problems is built-up from simpler optimisation problems. For the terminal wealth problem with constant loss-ratio the optimal premium strategy can be found analytically. For the total wealth problem the optimal relative premium is found to increase with the insurer’s risk aversion which leads to reduced market exposure and lower overall wealth generation

A unified pricing of variable annuity guarantees under the optimal stochastic control framework

In this paper, we review pricing of variable annuity living and death guarantees offered to retail investors in many countries. Investors purchase these products to take advantage of market growth and protect savings. We present pricing of these products via an optimal stochastic control framework, and review the existing numerical methods. For numerical valuation of these contracts, we develop a direct integration method based on Gauss-Hermite quadrature with a one-dimensional cubic spline for calculation of the expected contract value, and a bi-cubic spline interpolation for applying the jump conditions across the contract cashflow event times. This method is very efficient when compared to the partial differential equation methods if the transition density (or its moments) of the risky asset underlying the contract is known in closed form between the event times. We also present accurate numerical results for pricing of a Guaranteed Minimum Accumulation Benefit (GMAB) guarantee available on the market that can serve as a benchmark for practitioners and researchers developing pricing of variable annuity guarantees.Comment: Keywords: variable annuity, guaranteed living and death benefits, guaranteed minimum accumulation benefit, optimal stochastic control, direct integration metho

Alternative framework for the fair valuation of participating life insurance contracts

In this communication, we develop suitable valuation techniques for a with-profit/unitized with profit life insurance policy providing interest rate guarantees, when a jump-diffusion process for the evolution of the underlying reference portfolio is used. Particular attention is given to the mispricing generated by the misspecification of a jumpdiffusion process for the underlying asset as a pure diffusion process, and to which extent this mispricing affects the profitability and the solvency of the life insurance company issuing these contracts

Are the dimensions of private information more multiple than expected? Information asymmetries in the market of supplementary private health insurance in England

Our study reexamines standard econometric approaches for the detection of information asymmetries on insurance markets. We claim that evidence based on a standard framework with 2 equations, which uses potential sources of information asymmetries, should stress the importance of heterogeneity in the parameters. We argue that conclusions derived from this methodology can be misleading if the estimated coefficients in such an `unused characteristics' framework are driven by different parts of the population. We show formally that an individual's expected risk from the perspective of insurance, conditioned on certain characteristics (which are not used for calculating the risk premium), can equal the population's expectation in risk { although such characteristics are both related to risk and insurance probability, which is usually interpreted as an indicator of information asymmetries. We provide empirical evidence on the existence of information asymmetries in the market for supplementary private health insurance in the UK. Overall, we found evidence for advantageous selection into the private risk pool; ie people with lower health risk tend to insure more. The main drivers of this phenomenon seem to be characteristics such as income and wealth. Nevertheless, we also found parameter heterogeneity to be relevant, leading to possible misinterpretation if the standard `unused characteristics' approach is applied

Harnessing Health Care Markets for the Public Interest: Insights for U.S. Health Reform From the German and Dutch Multipayer Systems

Outlines how the German and Dutch systems offer universal coverage via competing insurance plans and promote effective and efficient care. Highlights insurance exchanges, multipayer policies and group purchasing, information systems, and public reporting

Monopoly, non-linear pricing, and imperfect information: a reconsideration of the insurance market

I reconsider Stiglitz's (1977) problem of monopolistic insurance with a continuum of types. Using a suitable transformation of control variables I obtain an analytical characterization of the optimal insurance policies. Closed form solutions and comparative statics results for special cases are provided

Optimal strategies for pricing general insurance

Optimal premium pricing policies in a competitive insurance environment are investigated using approximation methods and simulation of sample paths. The market average premium is modelled as a diffusion process, with the premium as the control function and the maximization of the expected total utility of wealth, over a finite time horizon, as the objective. In order to simplify the optimisation problem, a linear utility function is considered and two particular premium strategies are adopted. The first premium strategy is a linear function of the market average premium, while the second is a linear combination of the break-even premium and the market average premium. The optimal strategy is determined over the free parameters of each functional form. It is found that for both forms the optimal strategy is either to set a premium close to the break-even or not to sell insurance depending on the model parameters. If conditions are suitable for selling insurance then for the first premium strategy, in the case of no market average premium drift, the optimal premium rate is approximately ¯p(0)/aT above break-even where ¯p(0) is the initial market average premium, a is a constant related to the elasticity of demand and T is the time horizon. The optimal strategy for the second form of premium depends on the volatility of the market average premium. This leads to optimal strategies which generate substantial wealth since then the market average premium can be much larger than break-even leading to significant market exposure whilst simultaneously making a profit. Monte-Carlo simulation is used in order to study the parameter space in this case