Accuracy of numerical solutions using the eulers equation residuals

In this paper we derive sorne asymptotic properties on the accuracy of numerical solutions. We sIlow tIlat the approximation error of the policy function is of the same order of magnitude as the size of the Euler equation residuals. Moreover, for bounding this approximation error tIle most relevant parameters are the discount factor and the curvature of the return function. These findings provide theoretical foundations for the construction of tests that can assess the performance of alternative computational methods

VAR FOR QUADRATIC PORTFOLIO'S WITH GENERALIZED LAPLACE DISTRIBUTED RETURNS

This paper is concerned with the e±cient analytical computation of Value-at-Risk (VaR) for portfolios of assets depending quadratically on a large number of joint risk factors that follows a multivariate Generalized Laplace Distribution. Our approach is designed to supplement the usual Monte-Carlo techniques, by providing an asymptotic formula for the quadratic portfolio's cumulative distribution function, together with explicit error-estimates. The application of these methods is demonstrated using some financial applications examples.

Accuracy of numerical solutions using the eulers equation residuals.

In this paper we derive sorne asymptotic properties on the accuracy of numerical solutions. We sIlow tIlat the approximation error of the policy function is of the same order of magnitude as the size of the Euler equation residuals. Moreover, for bounding this approximation error tIle most relevant parameters are the discount factor and the curvature of the return function. These findings provide theoretical foundations for the construction of tests that can assess the performance of alternative computational methods.Accuracy; Euler equation residuals; value and policy functions;

Glosarium Matematika

273 p.; 24 cm

A Stochastic Linear Programming Model for Corn Residue Supply

This paper presents the results of a stochastic linear program for estimating the supply of corn residue for use as raw material in an ethanol plant. The model is based on the production capacity of an average Illinois farm, and considers the feasibility of three mutually exclusive residue harvesting alternatives. Since the potential for residue use in animal feed may be even more promising, these results are directly useful for the feed industry. They also indicate the profitability of investing in residue harvesting equipment. From a methodological point of view, the paper contrasts the results of three OR approaches. Because of the stochastic nature of the problem both Monte Carlo simulation and chance-constrained programming are found to be computationally viable, even though they differ in the way they incorporate risk information

Closed-Form Approximations for Spread Option Prices and Greeks

We develop a new closed-form approximation method for pricing spread options. Numerical analysis shows that our method is more accurate than existing analytical approximations. Our method is also extremely fast, with computing time more than two orders of magnitude shorter than one-dimensional numerical integration. We also develop closed-form approximations for the greeks of spread options. In addition, we analyze the price sensitivities of spread options and provide lower and upper bounds for digital spread options. Our method enables the accurate pricing of a bulk volume of spread options with different specifications in real time, which offers traders a potential edge in financial markets. The closed-form approximations of greeks serve as valuable tools in financial applications such as dynamic hedging and value-at-risk calculations.