Numerical integration of fully nonlinear size-structured population models

Characteristics' schemes of second order are introduced for the numerical solution of size-structured population models. The models are fully nonlinear: all the vital functions (growth, mortality and fertility rates) depend on the total population. The schemes are completely analysed: consistency, stability, existence and convergence are established. Some numerical experiments are also reported in order to show numerically the results proved in our analysis and to study the efficiency of a selection nodes technique.     

A Hamilton-Jacobi-Bellman approach to optimal trade execution

The optimal trade execution problem is formulated in terms of a mean-variance tradeoff, as seen at the initial time. The mean-variance problem can be embedded in a linear-quadratic (LQ) optimal stochastic control problem. A semi-Lagrangian scheme is used to solve the resulting nonlinear Hamilton-Jacobi-Bellman (HJB) PDE. This method is essentially independent of the form for the price impact functions. Provided a strong comparison property holds, we prove that the numerical scheme converges to the viscosity solution of the HJB PDE. Numerical examples are presented in terms of the efficient trading frontier and the trading strategy. The numerical results indicate that in some cases there are many different trading strategies which generate almost identical efficient frontiers.     

A numerically efficient closed-form representation of mean-variance hedging for exponential additive processes based on Malliavin calculus

ABSTRACT

We focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump-type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to the maturity. In this paper, we aim to derive a new explicit closed-form representation, which enables us to develop an efficient numerical method using the fast Fourier transforms. Note that our representation is described in terms of Malliavin derivatives. In addition, we illustrate numerical results for exponential Lévy models.     

Generalization of the weighted voting method using penalty functions constructed via faithful restricted dissimilarity functions

In this paper we present a generalization of the weighted voting method used in the exploitation phase of decision making problems represented by preference relations. For each row of the preference relation we take the aggregation function (from a given set) that provides the value which is the least dissimilar with all the elements in that row. Such a value is obtained by means of the selected penalty function. The relation between the concepts of penalty function and dissimilarity has prompted us to study a construction method for penalty functions from the well-known restricted dissimilarity functions. The development of this method has led us to consider under which conditions restricted dissimilarity functions are faithful. We present a characterization theorem of such functions using automorphisms. Finally, we also consider under which conditions we can build penalty functions from Kolmogoroff and Nagumo aggregation functions. In this setting, we propose a new generalization of the weighted voting method in terms of one single variable functions. We conclude with a real, illustrative medical case, conclusions and future research lines.     

Sections, selections and Prohorov's theorem

The famous Prohorov theorem for Radon probability measures is generalized in terms of usco mappings. In the case of completely metrizable spaces this is achieved by applying a classical Michael result on the existence of usco selections for l.s.c. mappings. A similar approach works when sieve-complete spaces are considered.     

Quadratic programming for portfolio optimization

Portfolio optimization is a procedure for generating a portfolio composition which yields the highest return for a given level of risk or a minimum risk for given level of return. The problem can be formulated as a quadratic programming problem. We shall present a new and efficient optimization procedure taking advantage of the special structure of the portfolio selection problem. An example of its application to the traditional mean-variance method will be shown. Formulation of the procedure shows that the solution of the problem is vector intensive and fits well with the advanced architecture of recent computers, namely the vector processor.     

Existence results for functional and neutral functional integrodifferential inclusions with lower semicontinuous right-hand side

In this paper, Schaefer's fixed point theorem combined with a selection theorem due to Bressan and Colombo is used to investigate the existence of solutions for the first- and second-order functional and neutral functional integrodifferential inclusions with lower semicontinuous and nonconvex-valued right-hand side.     

Parametric multiple regression risk models: Connections with tariffication,especially in motor insurance

It is shown how the parametric multiple regression risk models of Albrecht (1983a) can be used for solving the problem of tariffication of e.g. an motor insurance portfolio.     

Resonance-enhanced multiphoton ionization spectroscopy of CH3 and CD3. Two-photon absorption selection rules and rotational line strengths of the ν3- and ν4-active vibronic transitions

To explore the possibility of K-level resolved, 2+1 resonance-enhanced multiphoton ionization (REMPI) processes of the methyl radical, the two-photon absorption selection rules and rotational line strengths of the 3₀¹ and 4₀¹ vibronic bands of the transition (n=3 or 4) were reported. Stringent selection rules, which were imposed upon these two-photon transitions, are the initial K″=3p (p=0,1,2,…), ΔK=±2, ΔU=±3, and ΔN=0,±1,±2 (O, P, Q, R, and S branches). The previously assigned 2₂² vibronic band of the methyl radical should be studied by the REMPI with a better spectral resolution and analyzed by the newly derived two-photon absorption selection rules and rotational line strength formulas.     

On paraconvexity of graphs of continuous functions

The concept of paraconvexity of a subsetP E of a normed spaceE was first introduced by E. Michael. Roughly speaking, it consists of a controlled weakening of the convexity assumption forP, where the control is guaranteed via some parameter [0, 1). In this paper, we consider the case whenP is a subset of some (n+1)-dimensional Euclidean spaceE andP is the graph of some continuous functionf:V , whereV E is some convexn-dimensional subset ofE. Our key result is that paraconvexity of such a setP follows from the paraconvexity of sections ofP by two-dimensional planes, orthogonal toV. As an application, we prove a selection theorem for graph-valued mappings whose values have Lipschitzian (with a fixed constant) or monotone two-dimensional sections.Supported in part by the Ministry of Science and Technology of the Republic of Slovenia Research Grant No. P1-0214-101-93.Supported in part by G. Soros International Science Foundation.