The purpose of the talk is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. From one hand side stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control i...

We introduce explicitly the effort as a choice variable in a continuous time utility maximisation framework of an executive who is partly compensated with stock options. We solve the model in the case where the executive is not allowed to trade in the company’s stock but is able to achieve a partial insurance through trading in a correlated market portfolio. We define the executive’s value of t...

We study the existence and the properties of solutions to the Dirichlet problem for uniformly elliptic second-order Hamilton-JacobiBellman operators, depending on the principal eigenvalues of the operator.

We formulate a very general framework for optimal dynamic stochastic control problems which allows for a control-dependent informational structure. The issue of informational consistency is investigated. Bellman’s principle is formulated and proved. In a series of related results, we expound on the informational structure in the context of (completed) natural filtrations of stochastic processes.

Consider a stochastic process being controlled across a communication channel. The control signal that is transmitted across the control channel can be replaced by a malicious attacker. The controller is allowed to implement any arbitrary detection algorithm to detect if an attacker is present. This work characterizes some fundamental limitations of when such an attack can be detected, and quan...

This 1)aper addresses the stochastic modeling for managing asset liability process. We start with developing a jump-diffusion process for evaluating of the liabilities of the insurance company in general. We then tbrnmlate the ALM process into a stochastic control problem. With this approach, we present a Bel|man-Dreyfus Fundamental type formula for ALM process in terms of the solution of a sys...

In multiperiod control one sequentially chooses the value of an input variable to keep an output variable close to a target value. At any stage the input variable has to be such that the output is close to target while at the same time it provides as much information as possible about the model that relates input and output, to help keep the output close to target in the future. Certainty equiv...