Davide La Torre

Financial portfolio management through the goal programming model: Current state-of-the-art

Since Markowitz (1952) formulated the portfolio selection problem, many researchers have developed models aggregating simultaneously several conflicting attributes such as: the return on investment, risk and liquidity. The portfolio manager generally seeks the best combination of stocks/assets that meets his/her investment objectives. The Goal Programming (GP) model is widely applied to finance and portfolio management. The aim of this paper is to present the different variants of the GP model that have been applied to the financial portfolio selection problem from the 1970s to nowadays.

Approximating distribution functions by iterated function systems

In this small note an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Applications of this method to approximation of distribution functions and estimations are presented.

A generalized stochastic goal programming model

In this paper we show how one can get stochastic solutions of Stochastic Multi-objective Problem (SMOP) using goal programming models. In literature it is well known that one can reduce a SMOP to deterministic equivalent problems and reduce the analysis of a stochastic problem to a collection of deterministic problems. The first sections of this paper will be devoted to the introduction of deterministic equivalent problems when the feasible set is a random set and we show how to solve them using goal programming technique. In the second part we try to go more in depth on notion of SMOP solution and we suppose that it has to be a random variable. We will present stochastic goal programming model for finding stochastic solutions of SMOP. Our approach requires more computational time than the one based on deterministic equivalent problems due to the fact that several optimization programs (which depend on the number of experiments to be run) needed to be solved. On the other hand, since in our approach we suppose that a SMOP solution is a random variable, according to the Central Limit Theorem the larger will be the sample size and the more precise will be the estimation of the statistical moments of a SMOP solution. The developed model will be illustrated through numerical examples.

A cardinality constrained stochastic goal programming model with satisfaction functions for venture capital investment decision making

Venture capital has proven to be an essential resource for economic growth, especially in some technological clusters. The focus is on the way the venture capitalist makes the investment decision and the portfolio selection. The aim of this paper is to formulate the venture capital investment problem through the Goal Programming model where the Financial Decision-Maker’s preferences will be explicitly incorporated through the concept of satisfaction functions. The proposed model will be illustrated by using data from an Italian venture capital fund.

A Characterization of C^(k,1) Functions

In this work we provide a characterization of C{k,1} functions on Rn (that is k times differentiable with locally Lipschitzian k-th derivatives) by means of (k+1)-th divided differences and Riemann derivatives. In particular we prove that the class of C{k,1} functions is equivalent to the class of functions with bounded (k+1)-th divided difference. From this result we deduce aTaylors formula for this class of functions and a characterization through Riemann derivatives.

On Fractal Distribution Function Estimation and Applications

In this paper we review some recent results concerning the approximations of distribution functions and measures on [0,1] based on iterated function systems. The two different approaches available in the literature are considered and their relation are investigated in the statistical perspective. In the second part of the paper we propose a new class of estimators for the distribution function and the related characteristic and density functions. Glivenko-Cantelli, LIL properties and local asymptotic minimax efficiency are established for some of the proposed estimators. Via Monte Carlo analysis we show that, for small sample sizes, the proposed estimator can be as efficient or even better than the empirical distribution function and the kernel density estimator respectively. This paper is to be considered as a first attempt in the construction of new class of estimators based on fractal objects. Pontential applications to survival analysis with random censoring are proposed at the end of the paper.

A survey on C 1,1 fuctions: theory, numerical methods and applications

In this paper we survey some notions of generalized derivative for C 1,1 functions. Furthermore some optimality conditions and numerical methods for nonlinear minimization problems involving C1,1 data are studied.

Some Remarks on Second-order Generalized Derivatives for C wedge(1,1) Functions

Many definitions of second-order generalized derivatives have been introduced to obtain optimality conditions for optimization problems with C wedge(1,1) data. The aim of this note is to show some relations among these definitions.

Necessary Optimality Conditions for Nonsmooth Optimization Problems

In this paper we introduce a notion of generalized derivative for C wedge(1,1) vector functions in order to obtain necessary optimality conditions for vector optimization problems. This definition generalizes to the vector case the notion introduced by Yangand Jeyakumar.

Optimal control and long-run dynamics for a spatial economic growth model with physical capital accumulation and pollution diffusion

Abstract In this work we analyze the large-time behavior of a spatially structured economic growth model coupling physical capital accumulation and pollution diffusion. This model extends other results in the literature along different directions. Alongside the classical Cobb–Douglas production function, a convex–concave production function is considered. We add a negative feedback to the production function in order to describe the (negative) influence of pollution on output, and therefore on capital accumulation. We also present an optimal control problem for the above model.