Centro de Documentacion de Fundación MAPFRE - Fair valuation of insurance liability cash-flow streams in continuous time : applications

MAP20190019415

Fair valuation of insurance liability cash-flow streams in continuous time : applications / Lukasz Delong, Jan Dhaene and Karim Barigou

36 p.

Sumario: Delong et al. (2018) presented a theory of fair (market-consistent and actuarial) valuation of insurance liability cash-flow streams in continuous time. In this paper, we investigate in detail two practical applications of our theory of fair valuation. In the first example, we consider the fair valuation of a terminal benefit which is contingent on correlated tradeable and non-tradeable financial risks. In the second example, we consider a portfolio of unit-linked contracts contingent on a non-tradeable insurance and a tradeable financial risk. We derive partial differential equations (PDEs) which characterize the continuous-time fair valuation operators in these two examples and we find explicit solutions to these PDEs. The fair values of the liabilities are decomposed into the best estimate of the liability and a risk margin. The arbitrage-free representations of the fair values of the liabilities are derived and the dynamic hedging strategies associated with the continuous-time fair valuation operators are also established. Detailed interpretations of the results, which should be useful both for researchers and practitioners, are provided

En: Astin bulletin. - Belgium : ASTIN and AFIR Sections of the International Actuarial Association = ISSN 0515-0361. - 01/05/2019 Volumen 49 Número 2 - mayo 2019 , p. 299-333

1. Matemática del seguro . 2. Longevidad . 3. Valoración de riesgos . I. Dhaene, Jan . II. Barigou, Karim . III. Título.