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

Constructing continuum many countable, primitive, unbalanced digraphs

AbstractWe construct continuum many non-isomorphic countable digraphs which are highly arc transitive, have finite out-valency and infinite in-valency, and whose automorphism groups are primitive

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

Online educational counselling for students with special needs: Building rapport

This paper reports the findings from a study that investigated the effects of providing online counselling for undergraduate students with long‐term health problems. Issues associated with learning at a distance for such students include fatigue, manual dexterity, academic and social isolation, together with a need for better interactive communication with support agencies (Debenham, 1996a). The results of a feasibility study undertaken in 1996 suggested that for students with special needs personal rapport with their educational counsellor is considered important for problems to be aired and addressed (Debenham, 1998a). This raises interesting questions relating to how such rapport can be developed using computer‐mediated communication (CMC). Participants in the study reported appreciation of a small amount of informal contact with the counsellor in a closed peer‐group conference; this conference is described in Debenham (1996b). Building on this finding, a main study was undertaken which was modified by the addition of a counselling topic ‐ a ‘Virtual Study’ for the counsellor ‐ within this conference area (Debenham, 1998b). The counsellor was encouraged to participate informally in the other student‐led topics. This added a group dimension to the study. The results are encouraging: increased levels of motivation and enjoyment of the study process were reported by more than three‐quarters of the sample and in the degree of autonomy by more than half the sample. These findings throw light on the support of students with special needs and also contribute to the development of knowledge in the wider fields of academic advising and the use of CMC in distance education

Pricing general insurance with constraints

Deterministic control theory is used to find the optimal premium strategy for an insurer in order to maximise a given objective. The optimal strategy can be loss-leading depending on the model parameters, which may result in negative premium values. In such circumstances, it is optimal to capture as much of the market as possible before making a profit towards the end of the time horizon. In reality, the amount by which an insurer can lower premiums is constrained by borrowing restrictions and the risk inherent in building up a large exposure. Consequently, the effect of constraining the pricing problem is analysed with two forms of constraint: a bounded premium and a solvency requirement. If a lower bound is placed on the premium then an analytical solution can be found, which is not necessarily a smooth function of time. The optimal premium strategy is described in qualitative terms, without recourse to specifying particular parameter values, by considering the value of the terminal optimal premium. Solvency constraints lead to an optimisation problem which is coupled to the state equations and so there is no analytical solution. Numerical results are presented for a subset of the parameter space using control parameterisation, which turns the optimisation problem into a nonlinear programming problem

Crystallisation of PFA glasses

Bibliography: leaves 79-81.Glasses with various compositions, falling in the CaO-AI20rSi02 and MgO-CaOAI20rSi02 systems were made, using pulverised fuel ash and silica, hydrated lime, kaolin and magnesium carbonate. Titania or ferric oxide and chromia were used as nucleants. Various crystallisation heat treatments were carried out and the nucleation and crystallisation behaviour was studied. A minimum MgO:CaO was found to be necessary for bulk nucleation to occur. The activation energy for viscous flow decreased with increased MgO:CaO ratios. This was accompanied by an increase in the surface crystal growth rates and a decrease in the activation energy for surface crystal growth. Titania also lowered the activation energies for viscous flow and surface crystal growth and caused an increase in the surface crystal growth rates

Risks of Offline Verify PIN on Contactless Cards

Contactless card payments are being introduced around the world al- lowing customers to use a card to pay for small purchases by simply placing the card onto the Point of Sale terminal. Contactless transactions do not require veri- fication of the cardholder’s PIN. However our research has found the redundant verify PIN functionality is present on the most commonly issued contactless credit and debit cards currently in circulation in the UK. This paper presents a plausible attack scenario which exploits contactless verify PIN to give unlimited attempts to guess the cardholder’s PIN without their knowledge. It also gives experimental data to demonstrate the practical viability of the attack as well as references to support our argument that contactless verify PIN is redundant functionality which compromises the security of payment cards and the cardholder