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Optimality of general reinsurance contracts under CTE risk measure.
 Insurance: Mathematics and Economics
, 2011
"... a b s t r a c t By formulating a constrained optimization model, we address the problem of optimal reinsurance design using the criterion of minimizing the conditional tail expectation (CTE) risk measure of the insurer's total risk. For completeness, we analyze the optimal reinsurance model un ..."
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a b s t r a c t By formulating a constrained optimization model, we address the problem of optimal reinsurance design using the criterion of minimizing the conditional tail expectation (CTE) risk measure of the insurer's total risk. For completeness, we analyze the optimal reinsurance model under both binding and unbinding reinsurance premium constraints. By resorting to the Lagrangian approach based on the concept of directional derivative, explicit and analytical optimal solutions are obtained in each case under some mild conditions. We show that pure stoploss ceded loss function is always optimal. More interestingly, we demonstrate that ceded loss functions, that are not always nondecreasing, could be optimal. We also show that, in some cases, it is optimal to exhaust the entire reinsurance premium budget to determine the optimal reinsurance, while in other cases, it is rational to spend less than the prescribed reinsurance premium budget.
Optimal reinsurance subject to Vajda condition.
 Insurance: Mathematics and Economics
, 2013
"... h i g h l i g h t s • We explore optimal reinsurance that minimizes the value of an insurer's liability; • The insurer's liability is evaluated using a costofcapital approach; • We consider a class of ceded loss functions that are subject to Vajda condition; • Reinsurance premium princi ..."
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h i g h l i g h t s • We explore optimal reinsurance that minimizes the value of an insurer's liability; • The insurer's liability is evaluated using a costofcapital approach; • We consider a class of ceded loss functions that are subject to Vajda condition; • Reinsurance premium principles are assumed to preserve convex order; • We show that a piecewise linear ceded loss function is always optimal. a r t i c l e i n f o b s t r a c t In this paper, we study optimal reinsurance design by minimizing the riskadjusted value of an insurer's liability, where the valuation is carried out by a costofcapital approach based either on the value at risk or the conditional value at risk. To prevent moral hazard and to be consistent with the spirit of reinsurance, we follow
Optimal Reinsurance Analysis from a Crop Insurer's Perspective Title: Optimal Reinsurance Analysis from a Crop Insurer's Perspective
"... Purpose The primary objective of this paper is to analyze the optimal reinsurance contract structure from the crop insurer's perspective. Design/methodology/approach A very powerful and flexible empiricalbased reinsurance model is used to analyze the optimal form of the reinsurance treaty. ..."
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Purpose The primary objective of this paper is to analyze the optimal reinsurance contract structure from the crop insurer's perspective. Design/methodology/approach A very powerful and flexible empiricalbased reinsurance model is used to analyze the optimal form of the reinsurance treaty. The reinsurance model is calibrated to unique data sets including private reinsurance experience for Manitoba, and loss cost ratio experience for all of Canada, under the assumption of the standard deviation premium principle and conditional tail expectation risk measure. Findings The Vasicek distribution is found to provide the best statistical fit for the Canadian LCR data, and the empirical reinsurance model stipulates that a layer reinsurance contract structure is optimal, which is consistent with market practice. Research limitations/implications While the empirical reinsurance model is able to reproduce the optimal shape of the reinsurance treaty, the model produces some inconsistencies between the implied and observed attachment points. Future research will continue to explore the reinsurance model that will best recover the observed market practice. Practical implications Private reinsurance premiums can account for a significant portion of a crop insurer's budget, therefore, this study should be useful for crop insurance companies to achieve efficiencies and improve their risk management. Originality/value To the best of our knowledge, this the first paper to show how a crop insurance firm can optimally select a reinsurance contract structure that minimizes its total risk exposure, considering the total losses retained by the insurer, as well as the reinsurance premium paid to private reinsurers.
VaRbased Optimal Partial Hedging
"... Abstract. Hedging is one of the most important topics in finance. When a financial market is complete, every contingent claim can be hedged perfectly to eliminate any potential future obligations. When the financial market is incomplete, the investor may eliminate his risk exposure by superhedging. ..."
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Abstract. Hedging is one of the most important topics in finance. When a financial market is complete, every contingent claim can be hedged perfectly to eliminate any potential future obligations. When the financial market is incomplete, the investor may eliminate his risk exposure by superhedging. In practice, both hedging strategies are not satisfactory due to their high implementation costs which erode the chance of making any profit. A more practical and desirable strategy is to resort to the partial hedging which hedges the future obligation only partially. The quantile hedging of