2018/03/31 by Claudia Ceci, Ceci, Claudia, Katia Colaneri +3
Economics, Econometrics and Finance · Social Sciences · #60G35 #91B25 #91B30 #93E20 #FOS: Economics and business #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1804.00223
openalex publication_date 2018/03/31 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
In this paper we investigate the pricing problem of a pure endowment contract\nwhen the insurer has a limited information on the mortality intensity of the\npolicyholder. The payoff of this kind of policies depends on the residual life\ntime of the insured as well as the trend of a portfolio traded in the financial\nmarket, where investments in a riskless asset, a risky asset and a longevity\nbond are allowed. We propose a modeling framework that takes into account\nmutual dependence between the financial and the insurance markets via an\nobservable stochastic process, which affects the risky asset and the mortality\nindex dynamics. Since the market is incomplete due to the presence of basis\nrisk, in alternative to arbitrage pricing we use expected utility maximization\nunder exponential preferences as evaluation approach, which leads to the\nso-called indifference price. Under partial information this methodology\nrequires filtering techniques that can reduce the original control problem to\nan equivalent problem in complete information. Using stochastic dynamics\ntechniques, we characterize the indifference price of the insurance derivative\nvia the solutions of suitable backward stochastic differential equations.\n