Valuation of flexible insurance contracts. (English) Zbl 1117.62116

Melnikov, A. V.; Moliboga, M. M.; Skornyakova, V. S.

Teor. Jmovirn. Mat. Stat. 73, 97-103 (2005) and Theory Probab. Math. Stat., Vol 73, 109-115 (2006).

The character of flexible insurance contracts is determined by the presence of two sources of risk: mortality of the client and financial uncertainty of the securities market. Traditional insurance considers only the first source, reducing the second with the hypothesis of pre-determined future payments. Vice versa, in financial economics, the first factor is ignored, and future payments in reality depend on the evolution of the market during the contract period. The quantitative calculations of amounts of premiums and reserves for the innovative type of insurance must combine methods of actuarial and financial mathematics.
The authors of this paper give specific formulas for the value of policies of pure endowment with guarantee in the case where the security evolves according to the Black-Scholes model with constant and stochastic volatility. The basis for the approach comes from the methods of perfect hedging in complete markets and super hedging in incomplete ones. For more details see the book by A. V. Melnikov, S. N. Volkov and M. L. Nechayev [Mathematics of financial obligations, Vysshaya Shkola Ekonomiki, Moskva (2001)].

Reviewer: Mikhail P. Moklyachuk (Kyïv)

MSC:

62P05	Applications of statistics to actuarial sciences and financial mathematics
91B30	Risk theory, insurance (MSC2010)
91B28	Finance etc. (MSC2000)
60H30	Applications of stochastic analysis (to PDEs, etc.)

Keywords:

financial market; Black and Scholes formula; stochastic volatility