Subfair primitive casino with a discount factor

It is known that, for a subfair primitive casino, if a gambler has an initial fortune in (0, 1) and wishes to reach 1, then he should play boldly. Now if the game is modified by adding a discount factor which is used to motivate the gambler recognizing the time value of fortune and completing the game as quickly as is reasonably consistent with reaching the goal, then one would intuitively suspect that the gambler should still play boldly. However, this intuitive conjecture is false and the result of this paper goes in the opposite direction and states that the bold strategy need not be optimal for a subfair primitive casino with a discount factor.     

Uniform tail asymptotics for the aggregate claims with stochastic discount in the renewal risk models

Considering an insurer who is allowed to make risk-free and risky investments, as in Tang et al.(2010), the price process of the investment portfolio is described as a geometric L′evy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of extended regular variation, we obtain an asymptotically equivalent formula which holds uniformly for all time horizons, and furthermore, the same asymptotic formula holds for the finite-time ruin probabilities. The results extend the works of Tang et al.(2010).     

Enhanced alternating energy minimization methods for stochastic galerkin matrix equations

BIT Numerical Mathematics - In uncertainty quantification, it is commonly required to solve a forward model consisting of a partial differential equation (PDE) with a spatially varying uncertain...     

Cost minimization models: Applications in a teaching hospital

The primary objective of this article is to explore the feasibility of the application of cost minimization analysis in a teaching hospital environment. The investigation is concerned with the development of cost per admission and cost per patient day models. These models are further used for determining the value of the length of stay that would minimize cost per patient day (projected length of stay) and for estimating the costs. This study is based on total of 109,060 observations (2002), obtained from a teaching hospital in South Florida. The top 10 diagnosis-related groups (DRGs) with the highest volume are selected for the study. The cost models are fitted to the data for an average R² value of 87.3%, and a mean absolute percentage error (MAPE) value of 16.1%. The result demonstrates that if a hospital can control the length of stay at the projected level, on average, the cost per admission and the cost per patient day will decrease. Based on 8703 admissions for the selected DRGs in 2002, the total cost per year and the cost per patient day are decreased by approximately 8.56% ($15,453,841) and 4.02% ($66.30), respectively. Overall, these results confirm that the concept of cost minimization analysis in economic theory can be applied to healthcare industries for the purpose of reducing of costs. Cost minimization and cost variation analyses offer useful information to hospital management for better decision-making. It would be an important aid in making management decisions, particularly for cost reduction.     

Parallel deterministic and stochastic global minimization of functions with very many minima

The optimization of three problems with high dimensionality and many local minima are investigated under five different optimization algorithms: DIRECT, simulated annealing, Spall’s SPSA algorithm, the KNITRO package, and QNSTOP, a new algorithm developed at Indiana University.     

A parallel stochastic method for solving linearly constrained concave global minimization problems

A parallel stochastic algorithm is presented for solving the linearly constrained concave global minimization problem. The algorithm is a multistart method and makes use of a Bayesian stopping rule to identify the global minimum with high probability. Computational results are presented for more than 200 problems on a Cray X-MP EA/464 supercomputer.     

A comparison of different quantity discount pricing policies in a two-echelon channel with stochastic and asymmetric demand information

In this paper, we study quantity discount pricing policies in a channel of one manufacturer and one retailer. The paper assumes that the channel faces a stochastic price-sensitive demand but the retailer can privately observe the realization of an uncertain demand parameter. The problem is analyzed as a Stackelberg game in which the manufacturer declares quantity discount pricing schemes to the retailer and then the retailer follows by selecting the retail price and associated quantity. Proposed in the paper are four quantity-discount pricing policies: “regular quantity discount”; “fixed percentage discount”; “incremental volume discount” and “fixed marginal-profit-rate discount”. Optimal solutions are derived, and numerical examples are presented to illustrate the efficiency of each discount policy.     

Cost minimization of m simultaneous projects that require the same scarce resource

A company is responsible for m projects which are carried out concurrently. All m projects require the use of the same scarce resource for some time periods. An Integer Programming model is here presented to solve the problem of optimally allocating the scarce resource to the m projects so that the sum of total costs of carrying out the m projects is minimized.     

A stochastic periodic review integrated inventory model involving defective items, backorder price discount, and variable lead time

The purpose of this article is to investigate a stochastic integrated supplier-retailer inventory problem. The model analyzed in this article explores the problem of the protection interval, the backorder price discount, the lead time, and the numbers of shipments from the supplier to the retailer in one production run as control variables to widen applications for an integrated periodic review inventory model. We consider the situation in which the supplier and the retailer establish a long-term strategic partnership and contract to jointly determine the best strategy. We assume that the protection interval demand follows a normal distribution. Our objective is to determine the optimal review period, the optimal backorder price discount, the optimal lead time, and the optimal number of shipments from the supplier to the retailer in one production run, so that the joint expected annual total cost incurred has the minimum value. Furthermore, an algorithm of finding the optimal solution is developed. Also, the sensitivity analysis included and a numerical example is given to illustrate the results of the proposed model.     

Cost/risk balanced management of scarce resources using stochastic programming

We consider the situation when a scarce renewable resource should be periodically distributed between different users by a Resource Management Authority (RMA). The replenishment of this resource as well as users demand is subject to considerable uncertainty. We develop cost optimization and risk management models that can assist the RMA in its decision about striking the balance between the level of target delivery to the users and the level of risk that this delivery will not be met. These models are based on utilization and further development of the general methodology of stochastic programming for scenario optimization, taking into account appropriate risk management approaches. By a scenario optimization model we obtain a target barycentric value with respect to selected decision variables. A successive reoptimization of deterministic model for the worst case scenarios allows the reduction of the risk of negative consequences derived from unmet resources demand. Our reference case study is the distribution of scarce water resources. We show results of some numerical experiments in real physical systems.     

Infinite-horizon optimal controls for problems governed by a volterra integral equation with state-and-control-dependent discount factor

In this work, we concern ourselves with the existence of optimal solutions to optimal control problems defined on an unbounded time interval with states governed by a nonlinear Volterra integral equation. These results extend both the work of Baum and others in infinite-horizon control of ordinary differential equations as well as the work of Angell concerning integral equations. In addition, we incorporate into the objective functional (described by an improper integral) a discount factor which reflects a hereditary dependence on both state and control. In this manner, we are able to generalize the recent results of Becker, Boyd, and Sung in which they establish an existence theorem in the calculus of variations with objective functionals of the so-called recursive type. Our results are obtained through the use of appropriate lower-closure theorems and compactness conditions. Examples are presented in which the applicability of our results is demonstrated.This research was supported by the National Science Foundation, Grant No. DMS-87-00706.     

A new stochastic factor model: General explicit solutions

We present a new stochastic factor model. In doing so, we provide general, explicit solutions to the portfolio optimization problem.     

Weak minimization and duality

Sufficient and necessary optimality conditions are given for weakly minimized optimization problems in terms of a vector valued Lagrangian. Lagrangian and Wolfe type duals are constructed and duality established using an ordering that accords with the definition of a weak minimum. The results for differentiable problems continue to hold under weakened convexity assumptions and for problems which quasiminimize rather than minimize.     

Modifications in the discount sequence for bandit processes

For discrete–timeK-armed Bandit Processes with discounting, the value V(G,A) represents an observer's optimal expected gain using discount sequence A and prior distribution G on the distributions governing the K arms or processes being observed. In this paper we address the question of which types of modifications in the discount sequence will change the value in a predictable manner. Both positive and negative results are obtained. For example, it is shown that for two-armed bandits with one arm known, permutations of a positive term with a zero term in the discount sequence will change the value in a predictable way, but that this result can not be ex­tended to general two-armed bandits. We also show that there does not exist a ldquo;best information” arm in the sense that if the first term in each of two different discount sequences is zero then under G the same arm will be selected for each discount sequence     

Wealth optimization and dual problems for jump stock dynamics with stochastic factor

An incomplete financial market is considered with a risky asset and a bond. The risky asset price is a pure jump process whose dynamics depends on a jump-diffusion stochastic factor describing the activity of other markets, macroeconomics factors or microstructure rules that drive the market. With a stochastic control approach, maximization of the expected utility of terminal wealth is discussed for utility functions of constant relative risk aversion type. Under suitable assumptions, closed form solutions for the value functions and for the optimal strategy are provided and verification results are discussed. Moreover, the solution to the dual problems associated with the utility maximization problems is derived.