Premium allocation and risk avoidance in a large firm: a continuous model

Corporate wide risk pooling by a multi-divisional firm can reduce insurance costs through (i) economies of scale and (ii) properly motivating subsidiaries in managing their risk avoidance effort. Because of information asymmetry between the parent company and its subsidiaries, the firm faces the problem of devising implementable monitoring and premium (sharing) allocation schemes which provides an incentive for subsidiaries to control risk. This article develops an intra-corporate conceptual framework to premium allocation when claims and premium collection are defined in terms of continuous stochastic processes. The approach outlined is based on a principal-agent framework when the principal - the parent company, acts as an intermediary, returning to the agents - the subsidiaries, the benefits derived from risk aggregation. The problems arising from partial information regarding claims and loss prevention efforts are dealt with through a premium function which is sensitive to the liability accounts of subsidiaries, i.e., it reflects the residual claims collected net of premium payments made over time.