It is well known that in linear programming, the optimal values of the dual variables can be interpreted as shadow prices (marginal values) of the right-hand-side coefficients. However, this is true only under nondegeneracy assumptions. Since real problems are often degenerate, the output from conventional LP software regarding such marginal information can be misleading. This paper surveys and...

in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

The release of the January 1987 Consumer Price Index (cpi) in February will introduce updated market baskets that reflect population distributions from the 1980 census of population and spending patterns from the 1982-84 Consumer Expenditure Survey . This release will be part of a 5-year program to update the cpi market basket and incorporate numerous technical enhancements . t Although the cpi...

We propose a restructuring of U. S. Federal debt. All debt should be perpetual, paying coupons forever with no principal. The debt should be composed of the following: 1) Fixedvalue, floating-rate, electronically transferable debt. Such debt looks like a money-market fund, or reserves at the Fed, to an investor. 2) Nominal perpetuities. This debt pays a coupon of $1 per bond, forever. 3) Indexe...

Soctal Securtty checks dehvered to beneflclarles m the first week of July 1978 reflected the fourth automattc cost-of-ltvmg tncrease tn cash benefits under leglslatlon enacted tn 1972 and 1973 The 6 5-percent tncrease, which became effectwe to June, apphed to benefits for all persons on the social security benefit rolls at the end of Mdy, except those recetvmg benefits under the “spectal mmm~m ...

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study an approximation, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to...

This paper presents a new numerical method for pricing American call options when the volatility of the price of the underlying stock is stochastic. By exploiting a log-linear relationship of the optimal exercise boundary with respect to volatility changes, we derive an integral representation of an American call price and the early exercise premium which holds under stochastic volatility. This...

We use shifts in food Engel curves among the U.S. elderly to estimate the extent of Consumer Price Index (CPI) bias specific to this population. Over the last thirty years the share of total expenditure devoted to food has declined more rapidly for elderly-headed households than for other households. This decline is not explained by a more rapid increase in measured total expenditure for the el...

In this paper we consider the dynamics of spot and futures prices in the presence of arbitrage. We propose a partially linear error correction model where the adjustment coefficient is allowed to depend non-linearly on the lagged price difference. We estimate our model using data on the DAX index and the DAX futures contract. We find that the adjustment is indeed nonlinear. The linear alternati...