“Bounds for Ruin Probabilities in the Presence of Large Claims and their Comparison”, Vladimir Kalashnikov,April, 1999

Abstract

Performance measurement systems and report cards which attempt to measure and report the quality of care provided by managed health-care organizations, have become mainstream in health insurance markets as managed care penetration continues to increase. However, little is known about the impact formal plan evaluations have on the contracting and enrollment decisions made by health insurance purchasers and consumers. Information regarding the link between performance evaluations and enrollment is crucial for those charged with projecting future enrollments in and risk profiles of managed care organizations. This paper describes the performance measurement systems currently being used to evaluate managed care plans and reviews the empirical literature for evidence regarding the impact of measures on plan enrollments.     

Authors’ Reply: On the Time Value of Ruin - Discussion by F. Etienne De Vylder; Marc J. Goovaerts; David C.M. Dickson; Vladimir Kalashnikov; Gérard Pafumi

Abstract

The qualitative behavior of the optimal premium strategy is determined for an insurer in a finite and an infinite market using a deterministic general insurance model. The optimization problem leads to a system of forward-backward differential equations obtained from Pontryagin’s Maximum Principle. The focus of the modelling is on how this optimization problem can be simplified by the choice of demand function and the insurer’s objective. Phase diagrams are used to characterize the optimal control. When the demand is linear in the relative premium, the structure of the phase diagram can be determined analytically. Two types of premium strategy are identified for an insurer in an infinite market, and which is optimal depends on the existence of equilibrium points in the phase diagram. In a finite market there are four more types of premium strategy, and optimality depends on the initial exposure of the insurer and the position of a saddle point in the phase diagram. The effect of a nonlinear demand function is examined by perturbing the linear price function. An analytical optimal premium strategy is also found using inverse methods when the price function is nonlinear.