Hawkes processes in insurance: Risk model, application to empirical data and optimal investment
Anatoliy Swishchuk, Rudi Zagst, Gabriela Zeller
Abstract
In this paper we study a risk model with claim arrivals based on general compound Hawkes processes and show that it is suitable to model empirical insurance data. We review a law of large numbers and functional central limit theorem for this model and derive a pure diffusion approximation which allows analytical calculation of finite-time and infinite-time ruin probabilities. We use the approximation to study the influence of replacing the classical Poisson arrival process by a general compound Hawkes process on optimal investment strategies for an insurer in an incomplete market by applying results from asset–liability management.
Topics & Concepts
Limit (mathematics)Asset (computer security)EconometricsPoisson distributionCompound Poisson processInvestment (military)LiabilityCentral limit theoremHeavy traffic approximationActuarial scienceEconomicsMathematical economicsPoisson processApplied mathematicsMathematicsComputer scienceFinanceStatisticsMathematical analysisLawPoliticsComputer securityPolitical sciencePoint processes and geometric inequalitiesBayesian Methods and Mixture ModelsStatistical Methods and Bayesian Inference