Protected Valuation Portfolio
The valuation portfolio constructed in the previous chapter covers expected insurance liabilities and leads to best-estimate reserves for insurance liabilities. However to price insurance liabilities it is not sufficient to consider expected insurance liabilities. In general, a (risk averse) risk bearer of the insurance liabilities asks for an additional margin for settling the (non-hedgeable) insurance technical risks and for covering possible shortfalls in their development. The sum of the best-estimate reserves and this margin for non-hedgeable insurance technical risks then constitutes the so-called risk-adjusted reserves. In this chapter we give a methodological approach for the construction of risk-adjusted reserves. For this purpose we construct the protected valuation portfolio, which is a valuation portfolio protected against insurance technical risks. We give explicit numerical examples in terms of life and non-life insurance portfolios which provide interesting deeper insights. The core concept here is to choose appropriate probability distortions.
KeywordsCash Flow Spot Rate Insurance Liability Risk Aversion Parameter Conditional Tail Expectation
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