Andrew J. Heunis

Development of a new generation of interactive CACSD environments

A description is given of the development of a novel interactive computer-aided control system design (CACSD) package for the design of linear multivariable control systems. The package incorporates the stable factorization design technique and other recent design methodologies, such as the systematic design approach. To provide a high level of interactive design environment for the user, knowledge-based expert system development tools are provided within the package. In addition, the user is provided with the facilities to write user-defined functions and procedures. >

Convex duality in constrained mean-variance portfolio optimization

We apply conjugate duality to establish the existence of optimal portfolios in an asset-allocation problem, with the goal of minimizing the variance of the final wealth which results from trading over a fixed, finite horizon in a continuous-time, complete market, subject to the constraints that the expected final wealth equal a specified target value and the portfolio of the investor (defined by the dollar amount invested in each stock) take values in a given closed, convex set. The asset prices are modelled by Itô processes, for which the market parameters are random processes adapted to the information filtration available to the investor. We synthesize a dual optimization problem and establish a set of optimality relations, similar to the Euler-Lagrange and transversality relations of calculus of variations, giving necessary and sufficient conditions for the given optimization problem and its dual to each have a solution, with zero duality gap. We then solve these relations, to establish the existence of an optimal portfolio.

Rates of Convergence for an Adaptive Filtering Algorithm Driven by Stationary Dependent Data

Eweda and Macchi [IEEE Trans. Automat. Control, 29 (1984), pp. 119-127] and Watanabe [IEEE Trans. Inform. Theory, 30 (1984), pp. 134-140] show that the sequence of random vectors generated by a stochastic gradient adaptive filtering algorithm converges almost surely and in

Quadratic Risk Minimization in a Regime-Switching Model with Portfolio Constraints

L_p

Asymptotic properties of prediction error estimators in approximate system identification

(for

Law of the Iterated Logarithm for a Constant-Gain Linear Stochastic Gradient Algorithm

p

Averaging principle for diffusion processes

an even integer) to the solution of the associated Wiener-Hopf equation when the driving data process is stationary and weakly dependent. Under strong (i.e., Rosenblatt or

Strong diffusion approximations for recursive stochastic algorithms

\alpha

Rates of convergence in a central limit theorem for stochastic processes defined by differential equations with a small parameter

) and

On the Poisson equation for singular diffusions

\psi