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Optimal Insurance with Counterparty Default Risk

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Figure

Figure 1: Source: Guy Carpenter & Co., see Froot (2001)
Figure 2: The coinsurance set is given by X1 = X ′1 ∪ X ′′2 , the full insurance set by X2, and the noinsurance set by X3
Figure 3: Insurance coverage (I∗(x)) for different levels of fractional recovery. Assumptions: u(w) =−e−αw, with α = 0.05 (note that in this case the efficient contract does not depend on theinsurance buyer’s wealth distribution); A, W, X independent; A log-normally distributed, withA ∼ ln N(30, 15); X has Gamma distribution truncated at ¯x = 100 with mean 20 and standarddeviation 10; v = 30.
Figure 4: Insurance coverage as a fraction of the exposure (I∗(x)/x) for different levels of fractionalrecovery.

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