Recent developments in portfolio optimization via dynamic programming

Omole, Oluwakayode John
Optimal control is one of the benchmark methods used to handle portfolio optimization problems. The main goal in optimal control is to obtain a control process that optimizes the objective functional. In this thesis, we investigate optimal control problems for diffusion and jump-diffusion processes. Consequently, we present and prove concepts such as the Dynamic Programming principle, Hamilton-Jacobi-Bellman Equation and Verification Theorem. As an application of our results, we study optimization problems in finance and insurance. In this thesis, we use the Dynamic Programming approach to solve optimal control problems. In the applications, we provide a detailed study of optimal strategies that maximize the expected utility of investors and insurers in finite, random and infinite time horizons. In all applications considered, explicit solutions are obtained for the optimal value function and optimal control processes.


A Comparison of constant and stochastic volatility in Merton’s portfolio optimization problem
Öztürk, Ozan; Sezer, Ali Devin; Department of Financial Mathematics (2018)
Merton's Portfolio Problem is a dynamic portfolio choice problem, which assumes asset returns and covariances are constant. There is well documented evidence that, stock returns and volatilities are correlated. Therefore, stochastic volatility models in dynamic portfolio problems can give better results. The work [J. Liu, Portfolio selection in stochastic environments, Review of Financial Studies, 20(1), 2007] developed a general dynamic portfolio model that allows the parameters of the model to depend on a...
An Interactive approach to two-response product and process design optimization with statistical inferences
Özateş, Melis; Köksal, Gülser; Köksalan, Murat; Department of Industrial Engineering (2015)
In this study, an interactive approach has been developed for two-response product and process design optimization problems treating the single response problems as a special case. This approach considers preferences of the decision maker explicitly and the correlation between the responses. It uses a predefined set of objectives that are commonly encountered in the literature and industrial applications. However, instead of presenting all objective values at each iteration, a set of performance measures ar...
Comparative study on explicit integration algorithms for structural dynamics
Çakır, Dilara; Kurç, Özgür; Department of Civil Engineering (2022-8)
Conventional explicit integration algorithms used to solve structural dynamic problems may require too small time increments to satisfy the stability requirements in the presence of high-frequency modes. The requirement to have a too small time increment can cause extending the solution time above the tolerable limit. In this study, three different explicit integration algorithms found in the literature are compared in terms of stability, accuracy, and run-time. The examined integration methods are a two-st...
Stochastic dynamic programming based resource allocation for multi target tracking for electronically steered antenna radar /
Uzun, Çağlar; Demirekler, Mübeccel; Department of Electrical and Electronics Engineering (2015)
In this work, the concept of sensor management is introduced and stochastic dynamic programming based resource allocation approach is proposed to track multiple targets. The core of this approach is to use Lagrange relaxation for decreasing the state space dimension. By this approximation, the overall problem is separated into components instead of using joint Markov model to optimize large scale stochastic control problem. The aim of this study is to adaptively allocate radar resources in an optimal way in...
An Analysis of the Bidirectional LMS Algorithm over Fast-Fading Channels
Yapici, Yavuz; Yılmaz, Ali Özgür (2012-07-01)
A bidirectional LMS algorithm is considered for estimation of fast frequency-selective time-varying channels with a promise of near optimal tracking performance and robustness to parameter imperfections under various scenarios at a practical level of complexity. The performance of the algorithm is verified by the theoretical steady-state MSE analysis and experimental bit error rate (BER) results.
Citation Formats
O. J. Omole, “Recent developments in portfolio optimization via dynamic programming,” M.S. - Master of Science, Middle East Technical University, 2015.