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

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 max...

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Bibliographic Details
Published inMathematics and financial economics Vol. 11; no. 2; pp. 173 - 188
Main Authors Pennanen, Teemu, Perkkiö, Ari-Pekka, Rásonyi, Miklós
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2017
Springer Nature B.V
Subjects
Applications of Mathematics
Dynamic programming
Economic theory
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Expected utility
Finance
Insurance
Macroeconomics/Monetary Economics//Financial Economics
Management
Mathematical analysis
Mathematical functions
Mathematics
Mathematics and Statistics
Optimization
Quantitative Finance
Random variables
Statistics for Business
Studies
Utility functions
Non-convex optimization
Non-concave utility functions
Illiquidity
G11
Market frictions
Dynamic programming
C61
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Summary: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.
ISSN:1862-9679
1862-9660
DOI:10.1007/s11579-016-0176-6