Quantile hedging for guaranteed minimum death benefits with regime switching. (English) Zbl 1251.91041
Summary: The efficient hedging minimizes the average of the shortfall risk weighted by a loss function, where the hedging efficiency refers to the effectiveness of a hedge to accomplish the desired goal of risk management. Quantile hedging refers to the percentage of the hedge that can cover the contingent claim, which plays a key role for contingent claims in incomplete markets when perfect hedging is not possible. As observed in [H. Föllmer and P. Leukert, Finance Stoch. 3, No. 3, 251–273 (1999; Zbl 0977.91019)], the concept of quantile hedging can be considered as a dynamic version of the familiar value at risk concept (VaR). Treating regime switching diffusion models, this article focuses on guaranteed minimum death benefits (GMDBs), which are present in many variable annuity contracts, and act as a form of portfolio insurance. The GMDBs cannot be perfectly hedged due to the mortality component and incompleteness resulting from the regime switching, and as a result, quantile hedges are developed. Numerical examples are also presented to illustrate our results.
MSC:
| 91B30 | Risk theory, insurance (MSC2010) |
| 91B70 | Stochastic models in economics |
| 91G80 | Financial applications of other theories |
| 93E20 | Optimal stochastic control |
Citations:
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