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By Mario V. Wuthrich, Hans Buhlmann, Hansjorg Furrer

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4). 2) this is the insurance contract condition. ✷ Remarks. 3 is our definition for solvency. Pay attention to the fact that there is not a unique definition for solvency, indeed the solvency rules slightly differ from country to country. Moreover, we could replace the economic accounting principle E by any other appropriate accounting rule A. • The accounting condition is necessary but not sufficient for solvency. e. the valuation portfolio is deterministic with respect to technical risks) or if there is technical risk involved, we consider the valuation portfolio protected against technical risks.

1) = Z (50) , . . , Z (54) , I, Put(51) I, (1 + i)1 , . . e. we have that the total number of different units equals 11. These units play the role of the basis (financial instruments) in which we measure the insurance liabilities. Step 2. Determine the number/amount of each unit. 3) where we have specified a basis of financial instruments (dimension) and the number of instruments we need to hold to replicate the insurance claims. 32 3 Valuation portfolio in life insurance Step 3. To obtain the (monetary) value of our cash flow we need to apply an accounting principle to the VaPo.

0, 1, 0, . . , 0)T ∈ RL . But this immediately implies that eδ = M (1i , 1; h∗ ). 32) for all i = 1, . . , L. Hence we have found an equivalent martingale measure for the discounted price processes. Remarks. • The parameter h∗ is called the risk-neutral Esscher transform parameter and the corresponding equivalent martingale measure F ∗ = Fh∗ (·, ·) = F (·, ·; h∗ ) the risk-neutral Esscher measure. • Since h∗ is unique we have that the risk-neutral Esscher measure is unique. e. the market is not necessarily complete.

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