Insurance, Reinsurance and Dividend Payment

2008/04/24 by Dan Goreac, Goreac, D.
Economics, Econometrics and Finance · Mathematics · #49L20 #60H30 #FOS: Economics and business #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0804.3900

openalex publication_date 2008/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to introduce an insurance model allowing reinsurance and dividend payment. Our model deals with several homogeneous contracts and takes into account the legislation regarding the provisions to be justified by the insurance companies. This translates into some restriction on the (maximal) number of contracts the company is allowed to cover. We deal with a controlled jump process in which one has free choice of retention level and dividend amount. The value function is given as the maximized expected discounted dividends. We prove that this value function is a viscosity solution of some first-order Hamilton-Jacobi-Bellman variational inequality. Moreover, a uniqueness result is provided.

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