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Showing papers by "J. Michael Harrison published in 1983"


Journal ArticleDOI
TL;DR: In this article, it was shown that the model is complete if and only if there exists a unique martingale measure, i.e., the model can be represented as a stochastic integral with respect to the discounted price process.

473 citations


Journal ArticleDOI
TL;DR: The optimality of a particular control limit policy is proved directly, with heavy reliance on the change of variable formula for semimartingales, to minimize the expected discounted sum of holding costs and control costs over an infinite planning horizon.
Abstract: A controller continuously monitors a storage system, such as an inventory or bank account, whose content Z = {Zt,t≥0} fluctuates as a (μ, σ2) Brownian motion in the absence of control. Holding costs are incurred continuously at rate h(Zt). At any time, the controller may instantaneously increase the content of the system, incurring a proportional cost of r times the size of the increase, or decrease the content at a cost of l times the size of the decrease. We consider the case where h is convex on a finite interval [α, β] and h = ∞ outside this interval. The objective is to minimize the expected discounted sum of holding costs and control costs over an infinite planning horizon. It is shown that there exists an optimal control limit policy, characterized by two parameters a and b (α ≤ a < b ≤ β). Roughly speaking, this policy exerts the minimum amounts of control sufficient to keep Zt ∈ [a, b] for all t ≥ 0. Put another way, the optimal control limit policy imposes on Z a lower reflecting barrier at a an...

273 citations


Journal ArticleDOI
TL;DR: This work proves the existence of an optimal control band policy and calculates explicitly the optimal values of the critical numbers ( q, Q, S) and aims to minimize expected discounted costs over an infinite planning horizon.
Abstract: Consider a storage system, such as an inventory or cash fund, whose content fluctuates as a (μ, σ2) Brownian motion in the absence of control. Holding costs are continuously incurred at a rate proportional to the storage level and we may cause the storage level to jump by any desired amount at any time except that the content must be kept nonnegative. Both positive and negative jumps entail fixed plus proportional costs, and our objective is to minimize expected discounted costs over an infinite planning horizon. A control band policy is one that enforces an upward jump to q whenever level zero is hit, and enforces a downward jump to Q whenever level S is hit (0 < q < Q < S). We prove the existence of an optimal control band policy and calculate explicitly the optimal values of the critical numbers (q, Q, S).

233 citations


Posted Content
TL;DR: In this paper, the authors consider a world in which pension funds may default, the cost of the associated risk of default is not borne fully by the sponsoring corporation, and there are differential tax effects.
Abstract: This paper considers a world in which pension funds may default, the cost of the associated risk of default is not borne fully by the sponsoring corporation, and there are differential tax effects. The focus is on ways in which the wealth of the shareholders of a corporation sponsoring a pension plan might be increased if the Internal Revenue Service (IRS) and the Pension Benefit Guaranty Corporation (PBGC) follow simple and naive policies. Under the conditions examined, the optimal policy for pension plan funding and asset allocation is shown to be extremal in a certain sense. This suggests that the IRS and the PBGC may wish to use more complex regulatory procedures than those considered in the paper.(This abstract was borrowed from another version of this item.)

60 citations