Jean-Philippe Chancelier

Risk-sensitive portfolio optimization with transaction costs

We develop methods of risk sensitive impulsive control theory in order to solve an optimal asset allocation problem with transaction costs and a stochastic interest rate. The optimal trading strategy and the risk-sensitized expected exponential growth rate of the investor’s portfolio are characterized in terms of a nonlinear quasi-variational inequality. This problem can then be interpreted as the ergodic IsaacHamilton-Jacobi equation associated with a min-max problem. We use a numerical method based on an extended two-stage policy iteration algorithm for min-max problems and provide numerical results for the case of two assets and one factor that is a Vasicek interest rate.

Dynamic programming complexity and application

The authors consider the solution of dynamic programming in the presence of uncertainty, as a method in the study of stochastic optimal control. They discuss the Howard algorithm (an iterative method), complexity, the full multigrid Howard algorithm, the Pandore expert system for stochastic control, and the use of the formal calculus.<<ETX>>

Introduction to Scilab

The Scilab language was initially devoted to matrix operations, and scientific and engineering applications were its main target. But over time, it has considerably evolved, and currently the Scilab language includes powerful operators for manipulating a large class of basic objects.

Modeling and Simulation in Scilab

One of the fundamental problems in many areas of science and engineering is the problem of modeling and simulation. Scilab provides a large array of tools for developing and simulating models of several types. For several of these tools it is possible to use them with abbreviated commands and default values of some parameters. However, to know how to choose the appropriate tools and how to get the kind of answers desired, it is often necessary to know something about how the algorithms are set up and what to do if there are difficulties.

Automatic Study in Stochastic Control

The purpose of this paper is to give an example of automatic generation of a complete study in stochastic control done by an expert system designed at INRIA by the authors. This study includes the: automatic choice of an algorithm automatic checking of the mathematical well posedness of the problem automatic generation of a numerical routine automatic test of this routine on a numerical example automatic generation of graphics automatic writing of a report describing all the obtained results.

An Expert System for Stochastic Control Problems: Automatic Report Generation

We present a prototype expert system for the treatment of stochastic control problems. The objective is to automate all the steps involved in the solution of such problems, using computer algebra, inference techniques and symbolic manipulations. The system, written in Macsyma, Lisp and Prolog, accepts input in natural language and in symbolic form; it carries out the basic analysis of the problem, makes theoretical analyses to study the existence and uniqueness of solutions and selects a method among: Dynamic Programming, Optimization in the class of local feedbacks, Monte Carlo or Stochastic Gradient method, Perturbation method. The system generates a Fortran code for the numerical solution of the problem and finally a report including a description of the method and graphs for the numerical results. In this paper, we emphasize the automatic generation of the report.

Dual effect free stochastic controls

In stochastic optimal control, a key issue is the fact that “solutions” are searched for in terms of “closed-loop control laws” over available information and, as a consequence, a major potential difficulty is the fact that present control may affect future available information. This is known as the “dual effect” of control. Our main result consists in characterizing the maximal set of closed-loop control laws containing open-loop ones and for which the information provided by observations closed with such a feedback remains fixed. We give more specific results in the two following cases: multi-agent systems and discrete time stochastic input-output systems with dynamic information structure.

Systems and Control Toolbox

This chapter describes the main functions available in Scilab for system analysis and control. The basic functions that require speed and reliability are made of built-in primitives coded in C or Fortran, and the specialized functions are coded in the Scilab language.

Using Premia and Nsp for constructing a risk management benchmark for testing parallel architecture

Financial institutions have massive computations to carry out overnight, which are very CPU demanding. The challenge is to price many different products on a cluster‐like architecture. We have used the Premia software to valuate the financial derivatives. In this work, we explain how Premia can be embedded into Nsp, a scientific software like MATLAB, to provide a powerful tool to valuate a whole portfolio. Finally, we have integrated an Message Passing Interface (MPI) toolbox into Nsp to enable the use of Premia to solve a bunch of pricing problems on a cluster. This unified framework can then be used to test different parallel architectures. Copyright

Identification of pollution sources in rivers

This paper presents an application of the sentinels theory to an identification problem of pollution sources in rivers. A simplified model of the river dynamics is presented and the estimation problem is stated. The discrete problems which are to be numerically solved are then enumerated and the advantages of using the Scilab CASD package in order to solve them are pointed out.