Existence of solutions in non-convex dynamic programming and optimal investment

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• 作者：Teemu Pennanen ; Ari-Pekka Perkkiö ; Miklós Rásonyi
• 关键词：Non ; convex optimization ; Dynamic programming ; Non ; concave utility functions ; Market frictions ; Illiquidity
• 刊名：Mathematics and Financial Economics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：11
• 期：2
• 页码：173-188
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Quantitative Finance; Finance, general; Macroeconomics/Monetary Economics//Financial Economics; Economic Theory/Quantitative Economics/Mathematical Methods; Applications of Mathematics; Statistics for
• 出版者：Springer Berlin Heidelberg
• ISSN：1862-9660
• 卷排序：11

文摘

We establish the existence of minimizers in a rather general setting of dynamic stochastic optimization in finite discrete time without assuming either convexity or coercivity of the objective function. We apply this to prove the existence of optimal investment strategies for non-concave utility maximization problems in financial market models with frictions, a first result of its kind. The proofs are based on the dynamic programming principle whose validity is established under quite general assumptions.