This paper studies optimal switching on and off of the entire service capacity of an M/M/∞ queue with holding, running and switching costs. The running costs depend only on whether the system is on or off, and the holding costs are linear. The goal is to minimize average costs per unit time. The main result is that an average-cost optimal policy either always runs the system or is an (M, N)-policy defined by two thresholds M and N, such that the system is switched on upon an arrival epoch when the system size accumulates to N and is switched off upon a departure epoch when the system size decreases to M. It is shown that this optimization problem can be reduced to a problem with a finite number of states and actions, and an average-cost optimal policy can be computed via linear programming. An example, in which the optimal (M, N)-policy outperforms the best (0, N)-policy, is provided. Thus, unlike the case of single-server queues studied in the literature, (0, N)-policies may not be average-cost optimal.

We analyze a continuous review inventory model with the marginal carrying cost of a unit of inventory given by an increasing function of its shelf age and the marginal delay cost of a backlogged demand unit by an increasing function of its delay duration. We show that, under a minor restriction, an (r, q)-policy is optimal when the demand process is a renewal process, and a state dependent (r, q)-policy is optimal when the demand is a Markov-modulated renewal process. We also derive various monotonicity properties for the optimal policy parameters r* and r* + q*.

Two stochastic knapsack problem (SKP) models are considered: the static broken knapsack problem (BKP) and the SKP with simple recourse and penalty cost problem. For both models, we assume: the knapsack has a constant capacity; there are n types of items and each type has an infinite supply; a type i item has a deterministic reward vi and a random weight with known distribution Fi. Both models have the same objective to maximize expected total return by finding the optimal combination of items, that is, quantities of items of each type to be put in knapsack. The difference between the two models is: if knapsack is broken when total weights of items put in knapsack exceed the knapsack's capacity, for the static BKP model, all existing rewards would be wiped out, while for the latter model, we could still keep the existing rewards in knapsack but have to pay a fixed penalty plus a variant cost proportional to the overcapacity amount. This paper also discusses the special case when knapsack has an exponentially distributed capacity.

We propose a method for approximating equivalent local volatility functions of stochastic volatility models. Enlightened by the theory of generalized Wiener functionals proposed by Watanabe and Yoshida (1987, 1992), our key technique is to propose a closed-form expansion of conditional expectations involving marginal distributions generated by stochastic differential equations. A numerical test and an illustration of application are provided to demonstrate the efficiency of our approach.

In this paper, we consider a financial market with an asset exposed to a risk inducing a jump in the asset price, and which can still be traded after the default time. We use a default-intensity modeling approach, and address in this incomplete market context the problem of maximization of expected utility from terminal wealth for logarithmic, power and exponential utility functions. We study this problem as a stochastic control problem both under full and partial information. Our contribution consists of showing that the optimal strategy can be obtained by a direct approach for the logarithmic utility function, and the value function for the power (resp. exponential) utility function can be determined as the minimal (resp. maximal) solution of a backward stochastic differential equation. For the partial information case, we show how the problem can be divided into two problems: a filtering problem and an optimization problem. We also study the indifference pricing approach to evaluate the price of a contingent claim in an incomplete market and the information price for an agent with insider information.

We propose a geometric mixed fractional Brownian motion model for the stock price process with possible jumps superimposed by an independent Poisson process. Option price of the European call option is computed for such a model. Some special cases are studied in detail.

In this paper, we carry out stochastic comparisons of the largest order statistics arising from multiple-outlier gamma models with different both shape and scale parameters in the sense of various stochastic orderings including the likelihood ratio order, star order and dispersive order. It is proved, among others, that the weak majorization order between the scale parameter vectors along with the majorization order between the shape parameter vectors imply the likelihood ratio order between the largest order statistics. A quite general sufficient condition for the star order is presented. The new results established here strengthen and generalize some of the results known in the literature. Numerical examples and applications are also provided to explicate the theoretical results.

The existence of a moment function satisfying a drift function condition is well known to guarantee non-explosiveness of the associated minimal Markov process (cf. [1,9]), under standard technical conditions. Surprisingly, the reverse is true as well for a countable space Markov process. We prove this result by showing that recurrence of an associated jump process, that we call the α-jump process, is equivalent to non-explosiveness. Non-explosiveness corresponds in a natural way to the validity of the Kolmogorov integral relation for the function identically equal to 1. In particular, we show that positive recurrence of the α-jump chain implies that all bounded functions satisfy the Kolmogorov integral relation. We present a drift function criterion characterizing positive recurrence of this α-jump chain.

Suppose that to a drift function V there corresponds another drift function W, which is a moment with respect to V. Via a transformation argument, the above relations hold for the transformed process with respect to V. Transferring the results back to the original process, allows to characterize the V-bounded functions that satisfy the Kolmogorov forward equation.