Abstmct-A direct application of commonly used synchronization primitives such as semaphores, monitors, or the Ada rendezvous can lead to uncontrolled priority inversion, a situation in which a higher priority job is blocked by lower priority jobs for an indefinite period of time. In this paper, we investigate two protocols belonging to the class of priority inheritance protocols, called the basic priority inheritance protocol and the priority ceiling protoool. We show that both protocols solve this uncontrolled priority inversion problem. In particular, the priority ceiling protocol reduces the worst case task blocking time to at most the duration of execution of a single critical section of a lower priority task. In addition, this protocol prevents the formation of deadlocks. We also derive a set of sufficient conditions under which a set of periodic tasks using this protocol is schedulable.

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Abstract. A general consumption/investment problem is considered for an agent whose actions cannot affect the market prices, and who strives to maximize total expected discounted utility of both consumption and terminal wealth. Under very general conditions on the nature of the market model and on the utility functions of the agent, it is shown how to approach the above problem by considering separately the two more elementary ones of maximizing utility of consumption only and of maximizing utility of terminal wealth only, and then appropriately composing them. The optimal consumption and wealth processes are obtained quite explicitly. In the case of a market model with constant coefficients,, the optimal portfolio and consumption rules are derived very explicitly in feedback form (on the current level of wealth).

Abstract. The problem of maximizing the expected utility from terminal wealth is well understood in the context of a complete financial market. This paper studies the same problem in an incomplete market containing a bond and a finite number of stocks whose prices are driven by a multidimensional Brownian motion process W. The coefficients of the bond and stock processes are adapted to the filtration (history) of W, and incompleteness arises when the number of stocks is strictly smaller than the dimension of W. It is shown that there is a way to complete the market by introducing additional "fictitious" stocks so that the optimal portfolio for the thus completed market coincides with the optimal portfolio for the original incomplete market. The notion of a "least favorable" completion is introduced and is shown to be closely related to the existence question for an optimal portfolio in the incomplete market. This notion is expounded upon using martingale techniques; several equivalent characterizations are provided for it, examples are studied in detail, and a fairly general existence result for an optimal portfolio is established based on convex duality theory.Key words, incomplete markets, portfolio processes, stochastic control, convex duality, utility maximization AMS(MOS) subject classifications, primary 93E20; secondary 60G44, 90A16, 49B601. Introduction. This paper studies the problem of an agent who receives a deterministic initial capital, which he must then invest in an incomplete market so as to maximize the expected utility of his wealth at a prespecified final time. The market consists of a bond and m stocks, the latter being driven by a d-dimensional Brownian motion. In such a model, incompleteness arises when m is strictly smaller than d. The market coefficients, i.e., the interest rate, the rates of stock appreciation, and the stock volatility coefficients, are random processes adapted to the full d-dimensional Brownian

This paper considers the problem of fixed priority scheduling of periodic tasks with arbitrary deadlines. A general criterion for the schedulability of such a task set is given. Worst case bounds are given which generalize the Liu and Layland bound. The results are shown to provide a basis for developing predictable distributed real-time systems.