Dissertation > Excellent graduate degree dissertation topics show

Optimal Consumption and Portfolio Problem with Regimes Switching under Knightian Uncertainty

Author: YuMinXiu
Tutor: FeiWeiYin
School: Anhui University of Engineering
Course: Applied Mathematics
Keywords: Knightian uncertainty portfolio Markovian switching dual the-ory martingale method α-maxmin expected utility HJB equation dynamic pro-gramming stochastic control
CLC: F014.5
Type: Master's thesis
Year: 2013
Downloads: 6
Quote: 0
Read: Download Dissertation

Abstract


The classical consumption and investment model is analyzed by Merton in the late1960s. Since then, this kind of problem has been one of the major research areas in mathematical finance. This paper deals with the problem of optimal consump-tion and investment under Knightian uncertainty. Here, we distinguish Knightian uncertainty and risk. Risk denotes the fact that the future development of the stock market is random but the agent knows which future scenarios are possible and knows their market measure. Knightian uncertainty denotes the fact that market participants usually do not know the market measure or at least not exactly. In this paper, the agent optimizes his consumption and investment strategy with respect to a robust utility functional.First, we consider the investment problem in a general semimartingale frame-work where the agent may invest in the stock market and receives additional random endowment.We find a solution to the investment problem by using the martingale method and the dual theory. We prove that under appropriate assumptions a unique solution to the investment problem exists and is characterized. Furthermore, we can deduce that the value functions of primal and dual problem are convex conjugate functions. After that, we consider a diffusion-jump-model where the coefficients de-pend on the state of a Markov chain and the investor is uncertain about the intensity of the underlying Poisson process. In this model we consider an agent with loga-rithmic utility function. We use the stochastic control method to derive the HJB equation. The solution to this HJB equation can be determined numerically and we show how thereby the optimal investment strategy can be computed.Second, we consider the consumption and investment problem in a general semimartingale market. Here, the agent can invest an initial capital and a random endowment. To find a solution to the consumption and investment problem we use the martingale method. We prove that under appropriate assumptions a unique solution to the investment problem exists and is characterized too. Furthermore, in a diffusion-jump-model we consider an agent with logarithmic and HARA utility function. For both we use the stochastic control method to derive the HJB equation. The solution to this HJB equation can be determined numerically and we show how thereby the optimal investment strategy can be computed.

Related Dissertations

  1. Construction and improvement of basic education reform process evaluation platform,G521
  2. Implementation Study of evaluation method of the high school IT courses,G633.67
  3. Design and Development of Electronic Learning Portfolio for Distance Learning,TP391.6
  4. The Application of Recording Portefolio Assessment to English Teaching in Primary School,G623.31
  5. Logic-based Web service composition Petri net modeling and analysis,TP393.09
  6. Ontology -based Semantic Web service matching and composition method,TP393.09
  7. The Research about the Collection Asset Management Plan’s Operation in China Security Market,F832.51
  8. Research on the Information Transfer Effect of Disadvantageous Announcements,F832.51;F224
  9. Waveform Selection Method Based on Adaptive Dynamic Programming,TN951
  10. Research on the Credit Risk Management of Mortgage-backed Securitization under Subprime Crisis,F832.4;F293.3
  11. The Construction of Comoposite Model Portfolio Fund and Research on Evaluation System,F830.59
  12. Multi-Objective Optimization Research in Portfolio Selection,F830.91
  13. Research on Decision of R & D Project Portfolio Based on Fuzzy Theory,F224
  14. Research on Project Portfolio Management Mode of the Teaching Study in SG Institute of Technology,G647
  15. Optimal Control Design for Nonlinear Stochastic Systems with Input Delay,O232
  16. Bearer of Chinese Semantic Value and Mode,H13
  17. Application of the Portfolio in the Discipline of Primary School Language,G623.2
  18. The Setting-up and Research of Portfolio in Chemistry Learning,G633.8
  19. A Study of Chinese Investor Sentiment and Stock Return,F224
  20. Integration Supply Chain Scheduling with Single Machine,F274
  21. Behavioral Statisitical Arbitrage on Chinese Stock Market,F224

CLC: > Economic > Economics > Basic problems of economics > Sectors of the economy > Consumption and accumulation
© 2012 www.DissertationTopic.Net  Mobile