Stochastic optimal control theory: new applications to finance and insurance

Akdoğan, Emre
In this study, the literature, recent developments and new achievements in stochastic optimal control theory are studied. Stochastic optimal control theory is an important direction of mathematical optimization for deriving control policies subject to timedependent processes whose dynamics follow stochastic differential equations. In this study, this methodology is used to deal with those infinite-dimensional optimization programs for problems from finance and insurance that are indeed motivated by the real life. Stochastic optimal control problems can be further treated and solved along different avenues, two of the most important ones of being (i) Pontryagin’s maximum principle together with stochastic adjoint equations (within both necessary and sufficient optimality conditions), and (ii) Dynamic Programming principle together with Hamilton-Jacobi-Bellman (HJB) equations (within necessary and sufficient versions, e.g., a verification analysis). Here we introduce the needed instruments from economics and from Ito calculus, such as the theory of jump-diffusion and Ĺevy processes. We then present Dynamic Programing Principle, HJB Equations, Verification Theorem, Sufficient Maximum Principle for stochastic optimal control of diffusions and jump diffusions, and we state some connections and differences between Maximum Principle and the Dynamic Programing Principle. As financial applications, we investigate mean-variance portfolio selection problem and Merton optimal portfolio and consumption problem. From actuarial sciences, we study the optimal investment and liability ratio problem for an insurer and the problem of purchase of optimal life insurance, optimal investment and consumption of a wage-earner within a market of severallife-insuranceproviders,respectively. Inourexamples,weshallrefertovarious utility functions such as exponential, power and logarithmic ones, and to different parameters of risk averseness. We provide some graphical representations of the optimal solutions to illustrate the theoretical results. The thesis ends with a conclusion and an outlook to future studies, addressing elements of information, memory and stochastic robust optimal control problems. 


Estimation and hypothesis testing in stochastic regression
Sazak, Hakan Savaş; Tiku, Moti Lal; İslam, Qamarul; Department of Statistics (2003)
Regression analysis is very popular among researchers in various fields but almost all the researchers use the classical methods which assume that X is nonstochastic and the error is normally distributed. However, in real life problems, X is generally stochastic and error can be nonnormal. Maximum likelihood (ML) estimation technique which is known to have optimal features, is very problematic in situations when the distribution of X (marginal part) or error (conditional part) is nonnormal. Modified maximum...
Tool-life modelling of carbide and ceramic cutting tools using multi-linear regression analysis
Amaitik, SM; Tasgin, TT; Kilic, SE (2006-02-01)
This paper presents a study for the development of tool-life models for machining operations by means of a statistical approach called multi-linear regression analysis. The study was applied to a milling process for machining SAE 121 cast iron in a factory without interrupting the mass production. Different cutting tool materials under dry conditions were used in the cutting tests. Several machining experiments were performed and mathematical models for tool life have been postulated by using least-square r...
Material Processuality: Alternative Grounds for Design Research
Tönük Kruıthof, Damla (Informa UK Limited, 2020-01-01)
This article opens discussion on the positivist epistemology underlying the understandings of materials in design research that have been brought along as a result of theory and methods inherited from engineering and psychology. Examining the ambitions of work that seeks to operationalize knowledge created by these methods in the design process, we propose that attending to the processuality of material forms is a more adequate way for design research to capture the multiplicity of materials. We develop thi...
Continuous optimization applied in MARS for modern applications in finance, science and technology
Taylan, Pakize; Weber, Gerhard Wilhelm; Yerlikaya, Fatma (2008-05-23)
Multivariate adaptive regression spline (MARS) denotes a tool from statistics, important in classification and regression, with applicability in many areas of finance, science and technology. It is very useful in high dimensions and shows a great promise for fitting nonlinear multivariate functions. The MARS algorithm for estimating the model function consists of two subalgorithms. We propose not to use the second one (backward stepwise algorithm), but we construct a penalized residual sum of squares for a ...
Stochastic surplus processes with VaR AND CVaR simulations in actuarial applications
Şimşek, Meral; Uğur, Ömür; Kestel, Sevtap Ayşe; Department of Actuarial Sciences (2016)
The theory of ruin is a substantial study for those who are interested in financial survival probability based on the patterns imposed by the surplus process, which determines the insurer’s capital balance at a given time. In other words, fluctuations in aggregate claims as well as premiums in such processes can be secured by a certain capital. In this study, we simulate various surplus processes under different claim sizedistribution assumptions and extend the analyses by adding perturbation of a Brownian mo...
Citation Formats
E. Akdoğan, “Stochastic optimal control theory: new applications to finance and insurance,” M.S. - Master of Science, Middle East Technical University, 2017.