Optimal Cross Hedging of Insurance Derivatives |
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Authors: | Stefan Ankirchner Alexandre Popier |
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Institution: | 1. Institut für Mathematik, Humboldt-Universit?t zu Berlin , Berlin, Germany;2. Laboratoire de Statistiques et Processus , Université du Maine , Le Mans, France |
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Abstract: | Abstract We consider insurance derivatives depending on an external physical risk process, for example, a temperature in a low dimensional climate model. We assume that this process is correlated with a tradable financial asset. We derive optimal strategies for exponential utility from terminal wealth, determine the indifference prices of the derivatives, and interpret them in terms of diversification pressure. Moreover, we check the optimal investment strategies for standard admissibility criteria. Finally, we compare the static risk connected with an insurance derivative to the reduced risk due to a dynamic investment into the correlated asset. We show that dynamic hedging reduces the risk aversion in terms of entropic risk measures by a factor related to the correlation. |
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Keywords: | Admissibility Climate risk Cross hedging Dynamic hedging Entropic risk measure Indifference price Insurance derivative Negatively correlated exposure Optimal investment strategy Weather derivative Weather risk |
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