On Optimal Strategies to Deal with Extreme Regimes in Insurance

Abstract

We study a risk model where the insurer’s profit at a finite time horizon τ₁ can be controlled by making a change of premium at an optimally chosen time τ < τ₁. In the fluid approximation limit, this probabilistic control problem converges in probability to a deterministic problem, which we solve for specific claim size distributions and a unimodal demand function.

Key Words:

• Fluid approximation
• large deviations
• optimal trajectories
• premium rate change
• risk models

Additional information

Notes on contributors

J. Aquilina

John Aquilina Obtained an M.Phil. in Statistical Science from Cambridge University in 2001. Since then, he has been doing Ph.D. research in finance at the University of Bath. Among his interests are consumption/investment equilibrium problems in stochastic economies and default correlation in credit risk models.

M. Kelbert

Mark Kelbert Reader in Statistics at European Business Management School, University of Wales-Swansea. His research interests include queueing theory, diffusions and branching diffusions on manifolds, and mathematical physics.

Y.M. Suhov

Yuri Suhov

Professor of Applied Probability at Department of Pure Mathematics and Mathematical Statistics, Cambridge University. His research interests include statistical physics, theory of queueing network, and applied probability.