Optimal reinsurance subject to Vajda condition

Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle

“…We take the infimum given by (14) as the function of β, and numerically investigate how sensitively the value of β will affect our optimal value. The corresponding numerical results are given by Figure 2 below.…”

“…Figure 2. The horizontal axis represents β, the vertical axis represents the optimal value given by (14). The Greek θ is set to be 0.1.…”

“…See, for instance, Cai, et al [5], Chi [6] and Cheung, et al [7]. Recently, the optimization criterion of minimization of a number of ingenious risk measures is also widely applied, see Kaluszka [8,9], Gajek and Zagrodny [10], Promislow and Young [11], Cai, et al [12], Balbás, et al [13], Cheung [14], Chi and Weng [15] and the references therein.…”

“…Cai, et al [12] and Cheung [14] considered the set of all the increasing and convex functions as their feasible ceded loss function class. While, Lu, et al [16] took the set of all the increasing and concave functions as their feasible ceded loss function class.…”

“…(c) Generalizing the risk measures. Using the VaR, CTE, AVaR, respectively, Hu, et al [25], Cai and Tan [26], Cai, et al [12], Cheung [14] and Chi and Tan [24] found the optimal reinsurance contract. In Asimit, et al [27], a quantile-based risk measure was adopted in accordance with the insurer's appetite.…”