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56
Scheduling Networks of Queues: Heavy Traffic Analysis of a TwoStation Network With Controllable Inputs
, 1988
"... Motivated by a factory scheduling problem, we consider the problem of input control (subject to a specified input mix) and priority sequencing in a multistation, multiclass queueing network with general service time distributions and a general routing structure. The objective is to minimize the long ..."
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Cited by 88 (7 self)
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Motivated by a factory scheduling problem, we consider the problem of input control (subject to a specified input mix) and priority sequencing in a multistation, multiclass queueing network with general service time distributions and a general routing structure. The objective is to minimize the longrun expected average number of customers in the system subject to a constraint on the longrun expected average output rate. Under balanced heavy loading conditions, this scheduling problem can be approximated by a control problem involving Brownian motion. Linear programming is used to reduce the
Optimal portfolio choice and the valuation of illiquid securities
 The Review of Financial Studies
, 2001
"... Traditional models of portfolio choice assume that investors can continuously trade unlimited amounts of securities. In reality, investors face liquidity constraints. I analyze a model where investors are restricted to trading strategies that are of bounded variation. An investor facing this type o ..."
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Cited by 78 (13 self)
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Traditional models of portfolio choice assume that investors can continuously trade unlimited amounts of securities. In reality, investors face liquidity constraints. I analyze a model where investors are restricted to trading strategies that are of bounded variation. An investor facing this type of illiquidity behaves very differently from an unconstrained investor. A liquidityconstrained investor endogenously acts as if facing borrowing and shortselling constraints, and one may take riskier positions than in liquid markets. I solve for the shadow cost of illiquidity and show that large price discounts can be sustained in a rational model. The brass assembled at headquarters at 7 a.m. that Sunday. One after another, LTCM's partners, calling in from Tokyo and London, reported that their markets had dried up. There were no buyers, no sellers. It was all but impossible to maneuver out of large trading bets.Wall Street Journal, November 16, 1998. 1.
The Russian option: Reduced regret
 Ann. Appl. Probab
, 1993
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 76 (3 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Risk vs. ProfitPotential; A Model for Corporate Strategy
 J. Econ. Dynam. Control
, 1996
"... A firm whose net earnings are uncertain, and that is subject to the risk of bankruptcy, must choose between paying dividends and retaining earnings in a liquid reserve. Also, different operating strategies imply different combinations of expected return and variance. We model the firm's cash re ..."
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Cited by 48 (1 self)
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A firm whose net earnings are uncertain, and that is subject to the risk of bankruptcy, must choose between paying dividends and retaining earnings in a liquid reserve. Also, different operating strategies imply different combinations of expected return and variance. We model the firm's cash reserve as the difference between the cumulative net earnings and the cumulative dividends. The first is a diffusion (additive), whose drift/volatility pair is chosen dynamically from a finite set, A. The second is an arbitrary nondecreasing process, chosen by the firm. The firm's strategy must be nonclairvoyant. The firm is bankrupt at the first time, T , at which the cash reserve falls to zero (T may be infinite), and the firm's objective is to maximize the expected total discounted dividends from 0 to T , given an initial reserve, x; denote this maximum by V (x). We calculate V explicitly, as a function of the set A and the discount rate. The optimal policy has the form: (1) pay no dividends if ...
Piecewiselinear diffusion processes
 Advances in Queueing
, 1995
"... Diffusion processes are often regarded as among the more abstruse stochastic processes, but diffusion processes are actually relatively elementary, and thus are natural first candidates to consider in queueing applications. To help demonstrate the advantages of diffusion processes, we show that ther ..."
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Cited by 44 (10 self)
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Diffusion processes are often regarded as among the more abstruse stochastic processes, but diffusion processes are actually relatively elementary, and thus are natural first candidates to consider in queueing applications. To help demonstrate the advantages of diffusion processes, we show that there is a large class of onedimensional diffusion processes for which it is possible to give convenient explicit expressions for the steadystate distribution, without writing down any partial differential equations or performing any numerical integration. We call these tractable diffusion processes piecewise linear; the drift function is piecewise linear, while the diffusion coefficient is piecewise constant. The explicit expressions for steadystate distributions in turn yield explicit expressions for longrun average costs in optimization problems, which can be analyzed with the aid of symbolic mathematics packages. Since diffusion processes have continuous sample paths, approximation is required when they are used to model discretevalued processes. We also discuss strategies for performing this approximation, and we investigate when this approximation is good for the steadystate distribution of birthanddeath processes. We show that the diffusion approximation tends to be good when the differences between the birth and death rates are small compared to the death rates.
Irreversible Investment
, 1998
"... This paper proposes, solves and characterizes a model of sequential irreversible investment by a firm facing uncertainty in technology, demand and price of capital. The solution can be found in closed form if simple (but not totally unrealistic) functional forms are assumed, and can be given an ..."
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Cited by 22 (0 self)
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This paper proposes, solves and characterizes a model of sequential irreversible investment by a firm facing uncertainty in technology, demand and price of capital. The solution can be found in closed form if simple (but not totally unrealistic) functional forms are assumed, and can be given an optimal stopping interpretation. The marginal revenue product of capital that induces additional investment is higher, under irreversibility, than the conventionally measured user cost of capital. In ergodic steady state, however, the former quantity is on average lower than the latter
The relaxed stochastic maximum principles in singular optimal control of diffusions
 SIAM J. Cont. and Opt
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A free boundary problem related to singular stochastic control
 In Applied Stochastic Analysis (London, 1989) 265–301. Stochastics Monogr. 5. Gordon and Breach
, 1991
"... A free boundary problem related to singular stochastic control ..."
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Cited by 15 (0 self)
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A free boundary problem related to singular stochastic control
Inside Information And Stock Fluctuations
, 1999
"... A model of an incomplete market with the incorporation of a new notion of "inside information" is posed. The usual assumption that the stock price is Markovian is modified by adjoining a hidden Markov process to the BlackScholes exponential Brownian motion model for stock fluctuations. ..."
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Cited by 13 (5 self)
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A model of an incomplete market with the incorporation of a new notion of "inside information" is posed. The usual assumption that the stock price is Markovian is modified by adjoining a hidden Markov process to the BlackScholes exponential Brownian motion model for stock fluctuations. The drift and volatility parameters take different values when the hidden Markov process is in different states. For example, it is 0 when there is no subset of the market which has or which believes it has, extra information. However, the hidden process is in state 1 when information is not equally shared by all, and then the behavior of the members in the subset causes increased fluctuations in the stock price. This model
Numerical Comparison of Controls and Verification of Optimality for Stochastic Control Problems
 J. Optim. Th. Appl
, 1997
"... . We provide two approaches to the numerical analysis of stochastic control problems. These analyses rely on linear programming formulations of the control problem and allow numerical comparison between controls and numerical verification of optimality. The formulations characterize the processes th ..."
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Cited by 13 (7 self)
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. We provide two approaches to the numerical analysis of stochastic control problems. These analyses rely on linear programming formulations of the control problem and allow numerical comparison between controls and numerical verification of optimality. The formulations characterize the processes through the moments of the induced occupation measures. We deal directly with the processes rather than with some approximations to the processes. Excellent software is readily available since the computations involve finite dimensional linear programs. Key words. stochastic control, linear programming, numerical comparison, numerical verification, moments, bounded follower. Abbreviated Title. Numerical Analysis of Stochastic Control Problems. AMS(MOS) subject classifications. 49M35, 90C05, 93E20, 93E25. 1. Introduction. The purpose of this paper is to provide a numerical method for comparing the efficiency of various controls and to present a verification approach to the solution of stoch...