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This paper describes a practical algorithm based on Monte Carlo simulation for the pricing of multi- dimensional American (i.e., continuously exercisable) and Bermudan (i.e., discretely exercisable) options. The method generates both lower and upper bounds for the Bermudan option price and hence gives valid confidence intervals for the true value. Lower bounds can be generated using any number of primal algorithms. Upper bounds are generated using a new Monte Carlo algorithm based on the duality representation of the Bermudan value function suggested independently in Haugh and Kogan (2004) and Rogers (2002). Our proposed algorithm can handle virtually any type of process dynamics, factor structure, and payout specification. Computational results for a variety of multifactor equity and interest-rate options demonstrate the simplicity and efficiency of the proposed algorithm. In particular, we use the proposed method to examine and verify the tightness of frequently used exercise rules in Bermudan swaption markets. [ABSTRACT FROM AUTHOR]

This paper considers "critical path" networks which are used for the planning and scheduling of projects that consist of well defined sequences of individual activities. When the number of activities is large, it becomes difficult to prepare a network for the project as one unit, and it may also be difficult to store the network in the high speed memory of a digital computer. Also, in the cases where there are two or more independent projects, which are weakly inter-related by common activities, the problem of efficient scheduling of all the projects becomes quite difficult. This paper presents a method to "tear" or "decompose" a project network into several subnetworks, schedule the subnetworks and then to put the subnetworks back together. A computational algorithm is first given for time-only networks; then two computational formulations are given for cost-time network of project subnetworks. The latter essentially generalize the algorithm due to Fulkerson, in order to handle piecewise linear, convex, cost-time curves for some or all of the activities. [ABSTRACT FROM AUTHOR]

This paper gives a detailed description of an algorithm for the solution of a specialized Linear Programming model, to be called the Machine Loading model. It is a generalization of the Transportation Problem, in that weighting factors are applied to the individual elements which form the row and column sums. For the Machine Loading model, the simplex method reduces to a specialized algorithm which generalizes the stepping stone method of the Transportation Problem [2], [3]. With the resulting generalized stepping stone method, it becomes practicable to solve many large-scale problems for which the direct application of the simplex method would be impracticable. The present paper is restricted to a discussion of the following topics: (I) the general characteristics of the model and its topological features; (ii) a detailed solution algorithm, including a consideration of degenerate cases and the use of a computer; (iii) a more restrictive capacitated model and the corresponding modifications to the solution algorithm; and (iv) the complete illustrative solution of a numerical example. The purpose is to aid interested readers in gaining familiarity with the algorithm and facility in the solution of numerical problems. No derivations or proofs will be included. [ABSTRACT FROM AUTHOR]

This paper explores the normative theory of simulation within the context of an optimization algorithm for a linear programming model of the experimental setting. The simulation is viewed as a random generalized mathematical function which provides an uncertain evaluation of any policy within a specified constraint set. A sequential experimental design aimed at identifying the feasible levels of the policy variables which provide the optimal level of expected response is presented and analyzed. The results of numerical tests of the proposed procedure are discussed. [ABSTRACT FROM AUTHOR]

In a discrete-event simulation, the information related to the events scheduled to occur in the future is kept in a data structure called the future event set (FES). In this paper, we study the interaction hold model a popular stochastic model for FES performance analysis, corresponding to the superposition of a (fixed) number of renewal processes. The general state-space Markov chain formed by the discrete-time process that keeps track, at event times, of the residual lifetimes is shown here to be recurrent in the sense of Harris, and its stationary distribution is obtained. Linked lists and indexed lists, two popular FESs, are investigated using this model. For the interaction hold model, we make rigorous certain published results as well as introduce new ones. For example, we derive the distribution of the relative position of the event to be inserted in the data structure. In the exponential case, our analytic and empirical results confirm that when events with relatively short lifetimes often get regenerated upon their occurrence, it is better to scan a list (or sublist) from its head rather than tail. In the same context and for indexed lists with sublists with constant sizes, our results suggest that subsequent sublists should be of larger sizes, i.e., the first sublist should contain the smallest number of records, the second sublist the second smallest number of records, etc. [ABSTRACT FROM AUTHOR]

Approaches like finite differences with common random numbers, infinitesimal perturbation analysis, and the likelihood ratio method have drawn a great deal of attention recently as ways of estimating the gradient of a performance measure with respect to continuous parameters in a dynamic stochastic system. In this paper, we study the use of such estimators in stochastic approximation algorithms, to perform so-called "single-run optimizations" of steady-state systems. Under mild conditions, for an objective function that involves the mean system time in a G//G/1 queue, we prove that many variants of these algorithms converge to the minimizer. In most cases, however, the simulation length must be increased from iteration to iteration; otherwise the algorithm may converge to the wrong value. One exception is a particular implementation of infinitesimal perturbation analysis, for which the single-run optimization converges to the optimum even with a fixed (and small) number of ends of service per iteration. As a by-product of our convergence proofs, we obtain some properties of the derivative estimators that could be of independent interest. Our analysis exploits the regenerative structure of the system, but our derivative estimation and optimization algorithms do not always take advantage of that regenerative structure. In a companion paper, we report numerical experiments with an M/M/1 queue, which illustrate the basic convergence properties and possible pitfalls of the various techniques. [ABSTRACT FROM AUTHOR]

The paper presents a heuristic for determining the path that maximizes the expected utility of a stochastic acyclic network. The focus is on shortest route problems where a general, nonlinear utility function is used to measure outcomes. For such problems, enumerating all feasible paths is the only way to guarantee that the global optimum has been found. Alternatively, we develop a reduction algorithm based on stochastic dominance to speed up the computations. Monte Carlo simulation is used to evaluate the approach. In all, 70 test problems comprising 20 to 60 nodes are randomly generated and analyzed. The results indicate that the heuristic produces significant computational saving as the size of the network grows, and that the quality of the reduced network solutions are better than those obtained from the original formulation. [ABSTRACT FROM AUTHOR]

A theory of equivalent integer programs is developed that shows that every all-integer integer programming problem is equivalent to infinitely many other integer programming problems. The equivalence is such that the solution to any one problem in the equivalence class determines the solution to every other problem in the class. Procedures to construct certain canonical problems in each equivalence class are described. The relationship of this theory to computational algorithms is discussed. [ABSTRACT FROM AUTHOR]

In this report, twenty-nine integer linear programming problems, ranging from very simple to apparently rather difficult, are introduced. The results of running these problems on four different computer codes, involving five distinct algorithms, are presented as both time and iteration data. A brief description of the codes used is also included. [ABSTRACT FROM AUTHOR]