Working PaperSeptember 14th, 2023
FiledSeptember 14th, 2023where dI ≥ dL is determined by E[(X − dI)+] = E[I(X)] (or, equivalently, E[X ∧ dI] = E[RI(X)]). Thus, we have E[U (WI(X))] ≤ E[U (W(x—dI )+ (X))]. Furthermore, according to the proof of The- orem 4.2 in Chi (2019), E[U (W(x—d)+ (X))] is a decreasing function of d over [d∗, M), where d∗ is defined in (3.2). Recalling that dL ≥ d∗, we conclude that I is no better than (x − dL)+.