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Dynamic Approaches For Some Time-inconsistent Optimization Problems.pdf

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Preview of Dynamic approaches for some time-inconsistent optimization problems
🔗 Source: dornsife.usc.edu
📊 Size: 389 KB
👤 Author: Chandrasekhar Karnam, Jin Ma, Jianfeng Zhang
⬇️ Downloads: 49

Summary

The main contribution introduces the concept of "dynamic utility" to transform time-inconsistent problems into time-consistent ones.

Key Points:

1. Time Inconsistency vs. Comparison Principle: The authors argue that time inconsistency is essentially equivalent to the lack of a comparison principle, a fundamental tool in stochastic control theory.

2. Three Approaches: They propose three methods to revive the Dynamic Programming Principle (DPP) in this setting:
- Duality Approach: Uses a dual problem to establish time consistency.
- Dynamic Utility Approach: Introduces a new utility function that makes the problem time-consistent.
- Master Equation Approach: Utilizes a master equation to derive time-consistent conditions.

3. Benchmark Model: The authors consider a stochastic controlled problem with multidimensional backward Stochastic Differential Equations (SDEs) as a benchmark, encompassing many existing time-inconsistent problems.

4. Implications: These approaches allow for solving the original static optimization problem (1.1) without assuming optimal controls, which are not always guaranteed to exist in stochastic control theory.

Significance:

The paper offers novel solutions to a fundamental problem in economics and finance, providing alternative methods to address time-inconsistent optimization problems using dynamic programming principles.

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  • File Format: PDF
  • File Size: 389 KB
  • Pages: 43
  • Language: EN
  • Author: Chandrasekhar Karnam, Jin Ma, Jianfeng Zhang
  • Total Downloads: 49
  • Last Updated: 2 weeks ago

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