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Some problems in actuarial finance involving sums of dependent risks. (English) Zbl 1076.62558

Summary: A trend in actuarial finance is to combine technical risk with interest risk. If \(Y_t\), \(t = 1,2,...\) denotes the time-value of money (discount factors at time \(t\)) and \(X_t\) the stochastic payments to be made at time \(t\), the random variable of interest is often the scalar product of these two random vectors \(V=\sum X_t Y_t\). The vectors \(\overset \rightharpoonup X\) and \(\overset\rightharpoonup Y\) are supposed to be independent, although in general they have dependent components. The current insurance practice based on the law of large numbers disregards the stochastic financial aspects of insurance. On the other hand, introduction of the variables \(Y_1, Y_2,...\). to describe the financial aspects necessitates estimation or knowledge of their distribution function.
We investigate some statistical models for problems of insurance and finance, including Risk Based Capital/Value at Risk, Asset Liability Management, the distribution of annuities, cash flow evaluations (in the framework of pension funds, embedded value of a portfolio, Asian options) and provisions for claims incurred, but not reported (IBNR).

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
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