We study an optimal high frequency trading problem within a market microstructure model aiming at a good compromise between accuracy and tractability. The stock price is modeled by a Markov Renewal Process (MRP) as described in [12], while market orders arrive in the limit order book via a point process correlated with the stock price, and taking into account the adverse selection risk. We appl...

First Riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. An analytical approximation of the solution of nonlinear differential Riccati equation is investigated using the Adomian decomposition method. An application in optimal control is presented. The solution in different order of approximations and different methods of approximat...

This paper, which is the natural continuation of [14], studies a class of optimal control problems with state constraints where the state equation is a differential equation with delays. In [14] the problem is embedded in a suitable Hilbert space H and the regularity of the associated Hamilton-Jacobi-Bellman (HJB) equation is studied. The goal of the present paper is to exploit the regularity r...

An Adaptive Dynamic Programming algorithm for nonlinear systems with unknown dynamics is developed. The algorithm is initialized with a positive definite cost functional / stabilizing control law pair (V0, k0) (coupled via the Hamilton Jacobi Bellman Equation). Given (Vi, ki), one runs the system using control law ki recording the state and control trajectories, with these trajectories used to ...

We investigate the Cauchy problem for a nonlinear parabolic partial differential equation of Hamilton–Jacobi–Bellman type and prove some regularity results, such as Lipschitz continuity and semiconcavity, for its unique viscosity solution. Our method is based on the possibility of representing such a solution as the value function of the associated stochastic optimal control problem. The main f...

Abstract. In this paper, we value hydroelectric power plant cash flows under a stochastic control framework, taking into consideration the implication of operational constraints such as ramping and minimum flow rate constraints for the purpose of environmental protection. The power plant valuation problem under a ramping constraint is characterized as a bounded stochastic control problem, resul...

In this paper we study a class of optimal dividend and investment problems assuming that the underlying reserve process follows the Sparre Andersen model, that is, the claim frequency is a “renewal” process, rather than a standard compound Poisson process. The main feature of such problems is that the underlying reserve dynamics, even in its simplest form, is no longer Markovian. By using the b...

This paper studies finite horizon portfolio management by optimally tracking a ratcheting capital benchmark process. It is assumed that the fund manager can dynamically inject into account such total dominates nondecreasing floor process at each intermediate time. The problem formulated to minimize cost of accumulated injection. We first transform original with constraints an unconstrained cont...

Recently in [8] an ergodic control problem for a class of diffusion processes, constrained to take values in a polyhedral cone, was considered. The main result of that paper was that under appropriate conditions on the model, there is a Markov control for which the infimum of the cost function is attained. In the current work we characterize the value of the ergodic control problem via a suitab...

The present paper investigates an optimal reinsurance-investment problem with Hyperbolic Absolute Risk Aversion (HARA) utility. is distinguished from other literature by taking into account the interests of both insurer and a reinsurer. allowed to purchase reinsurance Both reinsurer are assumed invest in one risk-free asset risky whose price follows Heston's SV model. Our aim seek investment-re...