Optimal reinsurance with general risk measures

By Alejandro Balbás, Beatriz Balbás, Antonio J. Heras. 2009

138 citations recorded by the source corpus.

This paper studies the optimal reinsurance problem when risk is measured by a general risk measure. Necessary and sufficient optimality conditions are given for a wide family of risk measures, including deviation measures, expectation bounded risk measures and coherent measures of risk. The optimality conditions are used to verify whether the classical reinsurance contracts (quota-share, stop-loss) are optimal essentially, regardless of the risk measure used. The paper ends by particularizing the findings, so as to study in detail two deviation measures and the conditional value at risk.

Subfields: Demography, Economics and Econometrics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/f83fefe261977ad5a8a1b4f37dc5400f88ac958c

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In Demography

In Economics and Econometrics

In Management Science and Operations Research

Citations in the corpus

Optimality of general reinsurance contracts under CTE risk measure (2011, background): “Other related contributions include Gajek and Zagrodny (2000, 2004), Promislow and Young (2005), Balbás et al. (2009) and the references therein.”
Optimal Reinsurance under VaR and CVaR Risk Measures: A Simplified Approach (2010, methodology): “It should be emphasized that Balbás et al. (2009) and Tan et al. (2011) also obtain the above result by using the Lagrangian approach.”
Optimal Reinsurance under Variance Related Premium Principles (2012, unknown): “Moreover, Kaluszka (2005) and Balbás et al. (2009) study the optimal reinsurance problems by assuming a class of convex principles of premium calculation, which contains the variance and standard deviation principles due to their convex and Gâteaux differentiable properties in Deprez and Gerber (198”
Optimal Reinsurance Revisited – A Geometric Approach (2010, methodology): “(2) Functions in F that minimize the above objective functions are called optimal ceded loss functions.”
Optimal reinsurance under risk and uncertainty (2015, unknown): “c1 = 7 c2 = 1 c3 = 6 c4 = 1 c5 = 6 x = H t ∈ (1, 2) ∪ (3, 4) x = 1 t ∈ (0, 1) ∪ (2, 3) ∪ (3, 5)”
Optimal Reinsurance with General Premium Principles (2013, unknown): “On the other hand, by using more general risk measures and also assuming convex premium principles, Balbás et al. (2009) show that the quota share reinsurance is barely optimal regardless of the objective functions, while a stop loss reinsurance treaty is much more easier to satisfy the optimality c”
Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles (2013, unknown): “By limiting the feasible ceded loss function within the class F , we will find the explicit solutions for the reinsurance optimization models (3) and (4).”
Optimal reinsurance designs based on risk measures: a review (2020, methodology): “In this article, we review several main contributions motivated by Cai and Tan (2007). Due to the limited space, we could not mention all the contributions in this direction. In fact, many other interesting extensions of Cai and Tan (2007) also have appeared in the literature. For instance, the opti”
Optimal reinsurance with expectile (2016, unknown): “See, for instance, Gajek & Zagrodny (2004), Huang (2006), Balbás et al. (2009), Young (1999), Cheung (2010), Asimit et al. (2013c), Chi & Meng (2013), Cheung et al. (2014b), and so on.”