The name is absent

Examining terms on the right hand side and using the definitions of V(X) and V^t(X), we get

Xc —cc ∞                                  Xc —cc ∞

I   V^,(c + v + u)fι(u)du g(v)dv = /       [   [—Bk — 2[c + v + u]]fι(u)du g(v)dv

∞ √—∞                        √—∞ √—∞

— [Bk + 2c]Φ Xc—--\+2^σ_υφ(^Xc—^-
σ σ_v J σ σ_v J

as well as

∞∞

V^,(c + r + v + u)f2(u)du g(v)dv = / I [—Bk — 2[c + r + v + u]]f2(u)du g(v)dv
X Xc—c — -∞

[Bk + 2c+2r] 1

—*i ⅛ )l

— 2σv φ(JX_σV(¹ )

and finally

V V (Xc + r + u)f2(u)du — f
— -∞                    — —∞

∖ ∖α — Bk[X_c + r + u] — [X_c + r + u]²] f2(u)du — f ∖α — Bk[X_c + u] — [X_c + u]²] fι(u)du
-∞                               -∞

Putting things together, the first-order condition becomes

δ—φ f —^c---ʌ ∖Bkr + 2X_cr + r² + σ,

σ_υ \ σ_υ y

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