## Matlab Asset Pricing Function Finsolve

Due to the common structure of the arbitrage pricing equation across a large class of financial assets, it is possible to write general procedures for asset pricing. Such a procedure, finsolve, for solving an arbitrage condition for an asset that pays no dividends is shown in below. The function requires five inputs, model, fspace, alg, snodes and N. The first input, model, is a structure variable with the following fields func the name of the problem definition file T the time to maturity of...

## Bellman Bioeconomic Model

1.1 Some Apparently Simple 1.2 An Alternative Analytic 2 Computer Basics and Linear Equations 8 2.1 Computer 2.2 Data Storage 2.3 Linear Equations and the L-U 2.4 Gaussian 2.5 Rounding 2.6 111 2.7 Special Linear 2.8 Iterative Bibliographic 3.1 Bisection 3.2 Function 3.3 Newton's 3.4 Quasi-Newton 3.5 Problems With Newton Methods 3.6 Choosing a Solution 3.7 Complementarity Problems 3.8 Complementarity Bibliographic 4 Finite-Dimensional Optimization 63 4.1 Derivative-Free 4.2 Newton-Raphson Method...

## Quasi Monte Carlo Integration

Although Monte-Carlo integration methods originated using insights from probability theory, recent extensions have severed that connection and, in the process, demonstrated ways in which the methods can be improved, Monte-Carlo methods rely on sequences xj with the property that Any sequence that satisfies this condition for arbitrary Eiemann integrable functions can be used to approximate an integral on o, b , Although the Law of Large Numbers assures us that this is true when the are...

## Computational Examples 941 Asset Replacement

Consider the asset replacement model of Section 8,2,1 assuming that an asset produces q a 50 2,5a 2,5a2 units of output in its ath period of operation, up to period a 10, and that the output price is p 2, Further assume that the replacement cost k is an exogenous continuous-valued first-order Markov process kt i g kt,et i k 7 kt k et i where et is i.i.d, normal 0, a2 . The collocation method calls for the analyst to select n basis functions j j and n collocation nodes , and form the value...

## Constrained Optimization

The simplest constrained optimization problem involves the maximization of an objective function subject to simple bounds on the choice variable According to the Karush-Kuhn-Tucker theorem, if is differentiate on o, 6 , then x is a constrained maximum for onlv if it solves the complementarity problem CP ',a,6 5 Conversely, if is concave and differentiate on o, b and x solves the complementarity problem CP f' x , a, b , then x is a constrained maximum of if additionally is strictly concave on...

## Job Search

An infinitely-lived laborer must make employment decisions in an environment with fluctuating wages and uncertain job security. At the beginning of each period, the laborer observes the current wage rate w. If the laborer is currently employed, he must decide whether to continue to work at the given wage or to quit. If the laborer is currently unemployed, he must decide whether to search for job to begin the following period. If the laborer works, he receives the going wage rate w, if he...

## Piecewise Polynomial Splines

Piecewise polynomial splines, or simply splines for short, are a rich, flexible class of functions that may be used instead of high degree polynomials to approximate a real-valued function over a bounded interval. Generally, an order k spline consists of series of kth order polynomial segments spliced together so as to preserve continuity of derivatives of order k 1 or less. The points at which the polynomial pieces are spliced together, lt v2 lt lt vp, are called the breakpoints of the spline....

## An Approximation Toolkit

Implementing routines for multivariate function approximation involves a number of bookkeeping details that are tedious at best. In this section we describe a set of numerical tools that take much of the pain out of this process. This toolbox contains several high-level functions that use a structured variable to store the essential information that defines the function space from which approximants are drawn. The toolbox also contains a set of middle-level routines that define the basis...

## Quasi Newton Methods

Quasi-Newton methods employ a similar strategy to the Newton-Raphson method, but replace the Hessian of the objective function or its inverse with a negative definite approximation, guaranteeing that function value can be increased in the direction of the Newton step. The most efficient quasi-Newton algorithms employ an approximation to the inverse Hessian, rather than the Hessian itself, in order to avoid performing a linear solve, and employ updating rules that do not require second...

## An Integration Toolbox

The Matlab toolbox accompanying the textbook includes four functions for computing numerical integrals for general functions. Each takes three inputs, n, a, and b and generates appropriate nodes and weights. The functions qnwtrap and qnwsimp imple- Figure 5,2 Fill in of the Neiderreiter Sequence ment the Newton-Cotes trapezoid and Simpson's rule methods, qnwlege implements Gauss-Legendre quadrature and qnwequi generates nodes and weights associated with either equidistributed or pseudo-random...

## Data Storage

Matlab's basic data type is the matrix, with a scalar just a 1 x 1 matrix and an n-veetor an n x 1 or 1 x n matrix, Matlab keeps track of matrix size by storing row and column information about the matrix along with the values of the matrix itself. This is a significant advantage over writing in low level languages like Fortran or C because it relieves one of the necessity of keeping track of array size and memory allocation. When one wants to represent an m, x n matrix of numbers in a computer...

## An Alternative Analytic Framework

The two problems discussed in the preceding section illustrate how even simple economic models cannot always be solved using standard mathematical techniques. These problems, however, can easily be solved to a high degree of accuracy using numerical methods. Consider the inverse demand problem. An economist who knows some elementary numerical methods and who can write basic Matlab code would have little difficulty solving the problem. The economist would simply write the following elementary...