On the pricing of equity linked-life insurance contracts in Gaussian financial environment. (English) Zbl 1102.91053

Melnikov, A. V.; Nachaev, M. L.

Teor. Jmovirn. Mat. Stat. 70, 94-100 (2004) and Theory Probab. Math. Stat. 70, 105-111 (2005).

Suppose that an insurance company has a portfolio of \(l\) insurance contracts. Every contract is associated with a random time \(\tau_i,i=1,\dots,l,\) of incident occurrence. The corresponding premium is distributed between financial assets in a way that guarantee the best correspondence between liabilities of the company and its capital \(V^{\pi}\). As a criterion of quality of financial portfolio \(\pi\) the mean variance distance \(E[(V^{\pi}_T-f_T)^2]\) is considered, where \(f_T\) is the claim that should be paid by the company at the terminal time \(T\). The insurance contract based on market’s price of a given asset \(S_t\) is called ‘equity-linked life-insurance contract’. This paper deals with pricing of such insurance contracts. The stock process follows a stochastic exponential model with respect to a given Gaussian martingale. The considered model gives a possibility to obtain unified formulas for the mean variance hedging and the corresponding premium for the Black-Scholes and Gaussian discrete time models.

MSC:

91B28	Finance etc. (MSC2000)
91B30	Risk theory, insurance (MSC2010)

Keywords:

hedging; (B,S)-market; contingent claim; insurance liability