Showing papers by "J. Michael Harrison published in 1993"
TL;DR: The current state of knowledge in this dynamic area of research is surveyed, including important open problems, on the formulation of Brownian models for networks with complex routing.
Abstract: This paper is concerned with Brownian system models that arise as heavy traffic approximations for open queueing networks. The focus is on model formulation, and more specifically, on the formulation of Brownian models for networks with complex routing. We survey the current state of knowledge in this dynamic area of research, including important open problems. Brownian approximations culminate in estimates of complete distributions; we present numerical examples for which complete sojourn time distributions are estimated, and those estimates are compared against simulation.
180 citations
TL;DR: In this article, the authors consider a Russian option, which pays $S_\tau$ dollars to its owner at whatever stopping time the owner may select, based on the optimal stopping analysis of Shepp and Shiryaev.
Abstract: Let $X = \{X_t,t \geq 0\}$ be the price process for a stock, with $X_0 = x > 0$. Given a constant $s \geq x$, let $S_t = \max\{s,\sup_{0\leq u \leq t} X_u\}$. Following the terminology of Shepp and Shiryaev, we consider a "Russian option," which pays $S_\tau$ dollars to its owner at whatever stopping time $\tau \in \lbrack 0,\infty)$ the owner may select. As in the option pricing theory of Black and Scholes, we assume a frictionless market model in which the stock price process $X$ is a geometric Brownian motion and investors can either borrow or lend at a known riskless interest rate $r > 0$. The stock pays dividends continuously at the rate $\delta X_t$, where $\delta \geq 0$. Building on the optimal stopping analysis of Shepp and Shiryaev, we use arbitrage arguments to derive a rational economic value for the Russian option. That value is finite when the dividend payout rate $\delta$ is strictly positive, but is infinite when $\delta = 0$. Finally, the analysis is extended to perpetual lookback options. The problems discussed here are rather exotic, involving infinite horizons, discretionary times of exercise and path-dependent payouts. They are also perfectly concrete, which allows an explicit, constructive treatment. Thus, although no new theory is developed, the paper may serve as a useful tutorial on option pricing concepts.
60 citations