The construction of <mml:math alttext="$J$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>J</mml:mi></mml:math>-variate distribution functions, introducing dependences among
<mml:math alttext="$J$" id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>J</mml:mi></mml:math> random variables and keeping fixed the <mml:math alttext="$J$" id="E4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>J</mml:mi></mml:math> marginal distribution functions, is important in the
development of theoretical and empirical statistical analysis. Here, a method for generating such
distribution functions is developed. Characteristics of the resulting distribution functions are
discussed. An application to discrete regression models is presented. The latter is specialized to
model choice of mode od transportation by travelers.

Yadlin A. Marisa

Construction of <svg style="vertical-align:-1.97925pt" height="13.6375" version="1.1" viewBox="0 0 7.8874998 13.6375" width="7.8874998" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path id="x1D43D" d="M434 650l-5 -28q-60 -8 -75 -20.5t-25 -69.5l-71 -395q-20 -107 -57.5 -168t-106.5 -94q-40 -18 -61 -20l-10 32q77 23 113 108q21 50 41 160l68 377q10 57 -1.5 69.5t-76.5 20.5l6 28h261z"/></g></svg>-variate distribution functions and applications to discrete decision models

In this review paper we summarise several nonparametric methods recently
applied to the pricing of financial options. After a short introduction to martingale-based
option pricing theory, we focus on two possible fields of application for nonparametric
methods: the estimation of risk-neutral probabilities and the estimation of the dynamics
of the underlying instruments in order to construct an internally consistent model.

R&#252;diger  Kiesel

Nonparametric statistical methods and the pricing of derivative securities

There are few techniques available for testing if modes take speci&#64257;ed values. We show that standard tests of location such as the t-test and the Wilcoxon test, which test for the mean and median respectively, can perform poorly as tests for modes when the data is other than unimodal and symmetric. Carolan and Rayner [1] proposed a score test of location for symmetric nonnormal data. We consider a family of distributions similar to those considered by Carolan and Rayner [1] and propose a test for the mode or modes of data from multimodal or skewed distributions and demonstrate by way of simulations that it is reasonably effective.

Anthony M. Carolan

J. C. W. Rayner

One sample tests for the location of modes of nonnormal data

The sample correlation coefficient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>R</mml:mi></mml:math> is almost universally used to estimate the
population correlation coefficient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03C1;</mml:mi></mml:math>. If the pair <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:mi>Y</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>
has a bivariate normal distribution, this
would not cause any trouble. However, if the marginals are nonnormal, particularly if they
have high skewness and kurtosis, the estimated value from a sample may be quite different from
the population correlation coefficient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03C1;</mml:mi></mml:math>.The bivariate lognormal is chosen as our case study for this robustness study. Two approaches
are used: (i) by simulation and (ii) numerical computations.Our simulation analysis indicates that for the bivariate lognormal, the bias in estimating <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03C1;</mml:mi></mml:math> can
be very large if <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>&#x03C1;</mml:mi><mml:mo>&#x2260;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>, and it can be substantially reduced only after a large number (three to four
million) of observations. This phenomenon, though unexpected at first, was found to be
consistent to our findings by our numerical analysis.

C. D. Lai

T. P. Hutchinson

Robustness of the sample correlation - the bivariate lognormal case

Three approaches in obtaining the closed-form solution of the Vasicek bond
pricing problem are discussed in this exposition. A derivation based solely on the distribution
of the short rate process is reviewed. Solving the bond price partial differential
equation (PDE) is another method. In this paper, this PDE is derived via a martingale
approach and the bond price is determined by integrating ordinary differential equations.
The bond pricing problem is further considered within the Heath-Jarrow-Morton (HJM)
framework in which the analytic solution follows directly from the short rate dynamics
under the forward measure.

Rogemar S. Mamon

Three ways to solve for bond prices in the Vasicek model

We analyze a queueing system in which customers can call in to request service. A proportion,  say <mml:math alttext="$1-p$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn><mml:mo>&#8722;</mml:mo><mml:mi>p</mml:mi></mml:math> of them on their arrival test the availability of the server. If the server is free the customer enters service immediately. Otherwise, if the service system is occupied, the customer joins a source of unsatisfied customers called the orbit. The remaining <mml:math alttext="$p$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math> proportion of the initial customers enter the orbit directly, without examining the state of the server. We consider two models characterized by the discipline governing the order of re-requests for service from the orbit. First, all the customers from the orbit apply at a fixed rate. Secondly, customers from the orbit are discouraged and reduce their rate of demand as more customers join the orbit. The arrival at and the demands from the orbit are both assumed to be according to the Poisson Process. However, the service times for both primary customers and customers from the orbit are assumed to have a general distribution. We calculate several characteristic quantities of these queueing systems.

K.  Farahmand

N.  Cooke

Single retrial queues with service option on arrival

Although a large literature exists on the repair and deterioration of machines, the
associated problem of maintenance schedules for deteriorating renewable facilities has been little
studied. These facilities include all those which can be restored to a near-new state by renovation
or rebuilding, so that the market value and performance of the facility depends on the current
state of repair rather than on the time since initial construction. This paper solves the general
deterministic problem of finding the optimal repair strategy for a depreciating renewable facility.
It is shown that the value of the facility should approach the level where a function defined as
the "nett internal return" is greatest. If the facility has a finite life before sale or demolition, an
adjustment to repair strategies should be made as the facility approaches this time, increasing
repairs where this permits a better sale price to be obtained, or discontinuing repairs if they are
not justified by scrap or market value. Solutions for a range of common depreciation functions
and for linear and quadratic repair cost functions are obtained. The optimal life of the facility
is determined at the time when nett "external" marginal return, which includes potential capital
gain or loss and opportunity cost of capital, falls to zero.

Joe  Flood

Optimal investment strategies for renewable facilities

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Advances in Decision Sciences