We consider a zero-sum game of optimal stopping in which each of the opponents has the right to stop a one dimensional diffusion process. There are two types of costs. The first is accumulated continuously at the rate H(Xt) where Xt is the current position of the process. In addition there is a cost associated with the stopping of the process. It is given by the function f1(x) for the first pla...

In this thesis, we study both local time and Malliavin calculus and their application to stochastic calculus and finance. In the first part, we analyze three aspects of applications of local time. We first focus on the existence of the generalized covariation process and give an approximation when it exists. Thereafter, we study the decomposition of ranked semimartingales. Lastly, we investigat...

We consider the problem of online learning of optimal control for repeatedly operated systems in the presence of parametric uncertainty. During each round of operation, environment selects system parameters according to a fixed but unknown probability distribution. These parameters govern the dynamics of a plant. An agent chooses a control input to the plant and is then revealed the cost of the...

In this paper, optimal control problem for processes represented by stochastic sequential machine is analyzed. Principle of optimality is proven for the considered problem. Then by using method of dynamical programming, solution of optimal control problem is found.

We seek to determine the optimal amount of the insurer’s investment in all types of assets for a small and closed economy. The goal is to detect the implications and contributions the risk seeker and risk aversion insurer commonly make and the effectiveness in the investment decision. Also, finding the optimum portfolio for each is the main goal of the present study. To this end, we adopted the...

This paper presents a version of the Certainty Equivalence Principle, usable for nonlinear, variable end-time, partial observation Zero-Sum Differential Games, which states that under the unicity of the solution to the auxiliary problem, optimal controllers can be derived from the solution of the related perfect observation game. An example is provided where in one region, the new extended resu...

We establish the equivalence of competitive industry equilibrium with a central planner’s decision problem under uncertainty, when investment is irreversible. The existence of industry equilibrium is derived, and it is shown that myopic behavior on the part of small agents is harmless, in the sense that it leads to the same decisions as full rational expectations do. Our model is set in continu...