Financial Engineering

A generalized semi-Markov scheme models the structure of a discrete event system, such as a network of queues. By studying combinatorial and geometric representations of schemes we find conditions for second-order properties—convexity/concavity, sub/supermodularity—of their event epochs and event counting processes. A scheme generates a language of easible strings of events. We show that monotonicity of the event epochs is equivalent to this language forming an antimatroid with repetition.

We establish stochastic monotonicity of the event epoch sequences of generalized semi-Markov processes through the structure of the generalized semi-Markov schemes on which they are based. Our main condition states, roughly, that the occurrence of more events in the short run never leads to the activation of less events in the long run.

Countable-state, continuous-time Markov chains are often analyzed through simulation when simple analytical expressions are unavailable. Simulation is typically used to estimate costs or performance measures associated with the chain and also characteristics like state probabilities and mean passage times. Here we consider the problem of estimating derivatives of these types of quantities with respect to a parameter of the process. In particular, we consider the case where some or all transition rates depend on a parameter.

This paper establishes connections between two derivative estimation techniques: infinitesimal perturbation analysis (IPA) and the likelihood ratio or score function method. We introduce a systematic way of expanding the domain of the former to include that of the latter, and show that many likelihood ratio derivative estimators are IPA estimators obtained in a consistent manner through a special construction. Our extension of IPA is based on multiplicative smoothing.

This paper concerns dynamic part dispatch decisions in electronic test systems with random yield. A discrete time, multiproduct, miltistage production system is used as a model for the test system with the objective to minimize the sum of inventory holding, backlogging, and overtime costs over a finite horizon. Exact results for such systems have been limited to either single-stage, multiple time period, or multistage, single time period problems with a single product. Here we develop two approximate policies: the linear decision rule, and the myopic resource allocation.

Infinitesimal perturbation analysis is a technique for estimating derivatives of performance indices from simulation or observation of discrete event systems. Such derivative estimates are useful in performing optimization and sensitivity analysis through simulation. A general formulation of finite-horizon perturbation analysis derivative estimates is given, and then sufficient conditions for their use is presented with a variety of queuing systems.

When futures contracts are settled with respect to underlying asset prices, received theory suggests that the differences between futures prices and implied forward prices (from the term structure) are strictly due to marking to market, ceteris paribus. Empirical evidence appears to indicate that such differences are small for contracts with short maturities. What happens when the futures contract settles to yields implied by future prices of underlying assets?

For 0<K'<K≤∞, we obtain a K'-capacity queue from a K-capacity queue through a random time change and a truncation, provided arrivals are Poisson or service is exponential. In the case of an M/G/1/K queue, the time change erases service intervals that begin with more than K' customers in the systems. This constructions yields a straightforward sample path proof of Keilson's result on the proportionality of the ergodic queue length probabilities in M/G/1/K queues.