Pricing General Insurance Using Optimal Control Theory

ASTIN Bulletin, Vol. 35, No. 2, pp. 427-453, 2005

Posted: 1 Feb 2007

See all articles by Paul Emms

Paul Emms

King's College London

Steven Haberman

City University London - Faculty of Actuarial Science

Abstract

Insurance premiums are calculated using optimal control theory by maximising the terminal wealth of an insurer under a demand law. If the insurer sets a low premium to generate exposure then profits are reduced, whereas a high premium leads to reduced demand. A continuous stochastic model is developed, which generalises the deterministic discrete model of Taylor (1986). An attractive simplification of this model is that existing policyholders should pay the premium rate currently set by the insurer. It is shown that this assumption leads to a bang-bang optimal premium strategy, which cannot be optimal for the insurer in realistic applications. The model is then modified by introducing an accrued premium rate representing the accumulated premium rates received from existing and new customers. Policyholders pay the premium rate in force at the start of their contract and pay this rate for the duration of the policy. It is shown that, for two demand functions, an optimal premium strategy is well-defined and smooth for certain parameter choices. It is shown for a linear demand function that these strategies yield the optimal dynamic premium if the market average premium is lognormally distributed.

Keywords: Competitive demand model, optimal premium strategies, maximum principle, Bellman equation

JEL Classification: C00, G22

Suggested Citation

Emms, Paul and Haberman, Steven, Pricing General Insurance Using Optimal Control Theory. ASTIN Bulletin, Vol. 35, No. 2, pp. 427-453, 2005. Available at SSRN: https://ssrn.com/abstract=959583

Paul Emms (Contact Author)

King's College London ( email )

Strand
London, England WC2R 2LS
United Kingdom

Steven Haberman

City University London - Faculty of Actuarial Science ( email )

London
United Kingdom

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