tailieunhanh - Optimal cross hedging of insurance derivatives

Revenue insurance accounts for more than half of all crop insurance policies (Figure 2). It began in 1997 as a buy-up option on a pilot basis for major crops. By 2003, acreage under revenue- based insurance exceeded acreage covered by APH policies. Revenue insurance combines the production guarantee component of crop insurance with a price guarantee to create a target revenue guarantee. Under revenue insurance programs, participating producers are assigned a target level of revenue based on market prices for the commodity and the producer’s yield history. A farmer who opts for revenue insurance can receive an indemnity payment when. | Optimal cross hedging of insurance derivatives Stefan Ankirchner Institut fur Mathematik Humboldt-Universitat zu Berlin Unter den Linden 6 10099 Berlin Germany Peter Imkeller Institut fuir Mathematik Humboldt-Universitait zu Berlin Unter den Linden 6 10099 Berlin Germany Alexandre Popier Laboratoire de statistiques et processus Universite du Maine Avenue Olivier Messiaen F-72085 Le Mans Cedex 9 France March 19 2007 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. 2000 AMS subject classifications primary 60H10 91B30 secondary 91B76 93E20 60H30. Key words and phrases insurance derivative dynamic hedging climate risk weather risk weather derivative indifference price optimal investment strategy admissibility entropic risk measure cross commodity hedging negatively correlated exposure. 1 1 Introduction In recent years financial risks originating in the uncertainties of weather and climate are gaining an increasing attention in insurance and banking. This is partly due to the public coverage changes in weather patterns obtain but also to the awareness that modern methods of stochastic finance offer new ways for dynamically transferring insurance risk to financial markets. Not only since the increasing activity in weather extremes such as big tropical .

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