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

Teemu Pennanen; Ari-Pekka Perkkioe; Miklos Rasonyi

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

机译：非凸动态规划中解决方案的存在与最优投资

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摘要

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.

机译：我们在有限的离散时间内在动态随机优化的相当一般的设置中建立了极小值的存在，而没有假设目标函数的凸性或矫顽性。我们以此来证明存在摩擦的金融市场模型中非凹型效用最大化问题的最优投资策略的存在，这是同类问题的第一个结果。证明基于动态编程原理，其有效性是在相当普遍的假设下确定的。

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来源
《Mathematics and financial economics》 |2017年第2期|173-188|共16页
作者
Teemu Pennanen; Ari-Pekka Perkkioe; Miklos Rasonyi;
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作者单位

Department of Mathematics, King's College London, Strand, London WC2R 2LS, UK;

Department of Mathematics, Technische Universitaet Berlin, Building MA, Str. des 17. Juni 136,10623 Berlin, Germany;

MTA Alfred Renyi Institute of Mathematics, Realtanoda utca 13-15, Budapest 1053, Hungary;

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正文语种 eng
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关键词
Non-convex optimization; Dynamic programming; Non-concave utility functions; Market frictions; Illiquidity;

机译：非凸优化;动态编程;非凹面效用函数;市场摩擦;非流动性;

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2. On the applicability and solution of bilevel optimization models in transportation science: A study on the existence, stability and computation of optimal solutions to stochastic mathematical programs with equilibrium constraints [J] . Michael Patriksson Transportation Research Part B: Methodological . 2008,第10期

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3. Optimality conditions for multiple objective fractional subset programming with (ρ, σ, θ)-type-I and related non-convex functions [J] . S. K. Mishra, M. Jaiswal, Pankaj Calcolo . 2012,第3期

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5. Approximate dynamic programming based solutions for fixed-final-time optimal control and optimal switching. [D] . Heydari, Ali. 2013

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6. The Optimal Solution of a Non-Convex State-Dependent LQR Problem and Its Applications [O] . Xudan Xu, J. Jim Zhu, Ping Zhang -1

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7. Existence of solutions in non-convex dynamic programming and optimal investment [O] . Pennanen T., Perkkiö A-P., Rásonyi Miklós 2017

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8. Optimal Control of Classical Molecular Dynamics: A Perturbation Formulation andthe Existence of Multiple Solutions [R] . Demiralp, M., Rabitz, H. 1994

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

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