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Chen, Yang ; Shuaijie, Qian. (2025) Non-Concave Utility Maximization with Transaction Costs.
In: Papers. RePEc:arx:papers:2307.02178.
Full description at Econpapers
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The proof of this proposition is identical with Dai et al. (2022), then Condition a) is verified by Corollary 5.6 of Bouchard and Touzi (2011). Appendix C.2 Verifying Condition b) In this part, we want to prove the continuity of value function around z = K. More precisely, we have the following result Proposition 5. We have lim (t,x,y)â(t0,xÌ,yÌ) V (t, x, y) = U(K), when zÌ = K. Proof of Proposition 5. On the one hand, it is easily found that lim inf (t,x,y)â(t0,xÌ,yÌ) V (t, x, y) ⥠U(K). On the other hand, denote by VÌ (t, z) the value function for given wealth z at time t and without transaction costs, we then have VÌ (t, x + (1 â θ1)y+ â (1 + θ2)yâ ) ⥠V (t, x, y).
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