Srdjan Stojanovic

Periodic optimal control for competing parabolic Volterra-Lotka-type systems

In this paper, we study the optimal harvesting control problem governed by a time-periodic competing parabolic Volterra-Lotka system. We show the existence of an optimal control, and we also find some conditions which enable the characterization of the optimal control in terms of a large parabolic optimality system. We further construct monotone sequences closing in to all appropriate solutions of the periodic optimality system.

Optimal damping control and nonlinear parabolic systemes

An optimal control problem for a parabolic equation when the control parameter is the zero order coefficient of the differential operator is considered. An optimality system is derived. Under a certain sign condition, the problem is solved completely, by proving uniqueness and providing a constructive existence proof for the nonlinear parabolic optimality system.

A minimax problem for semilinear nonlocal competitive systems

A two-sided game for the control of a stationary semilinear competitive system with autonomous sources is considered, where the controls are the kernels of the nonlocal interaction terms. The saddle point (the optimal solution of the game) is characterized as the unique solution of the associated optimality system, which is solved by an iterative scheme.

Optimal switching for systems governed by nonlinear evolution equations

Optimal switching for a nonlinear evolution equation is considered. A type of approximating problems with value functions {uu0<u<u0} is studied. We prove that each uu is the unique viscositY solution of corresponding Hami1ton-Jacoby system, uu convergesto the value function u of the original problem as µ goes to 0, and an optimal control is determined.

Neutral and Indifference Portfolio Pricing, Hedging and Investing

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MONOTONE ITERATIONS FOR NONLINEAR OBSTACLE PROBLEM

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Any-utility neutral and indifference pricing and hedging

The existence, uniqueness and regularity of solutions are proved for the obstacle problem with semilinear elliptic partial differential equations of second order. Computationally effective algorithms are provided and application made to steady state problem for the logistic population model with diffusion and an obstacle to growth.

A variational approach to a free boundary problem arising in electrophotography

Using recent, original approach, neutral and indifference pricing PDEs are derived for general multi-dimensional Markovian diffusive market models and, under certain conditions, for any utility of wealth. In the case of portfolios of contracts the pricing PDE system is proved for neutral, while conjectured and discussed for indifference pricing. Hedging formulas are given too. Some special cases are derived as well to demonstrate the consistency with the well known results.

Foreign Exchange Derivatives

A least square approach to a free boundary problem modeling the photocopying process posed by A. Friedman and B. Hu [4] is considered. The corresponding variational functional is nonconvex and nonsmooth, so that its generalized gradient is multivalued.

Pricing portfolios of contracts on cumulative temperature with risk premium determination

We establish general theory of foreign exchange derivatives (FXD), for multidimensional, possibly incomplete, Ito SDE market/econometric models. The established theory is consistent with the one of foreign exchange rates (FXR) introduced by the author in a previous note. A very simple example is presented as well.