EVALUATING THE PROSPECTS OF BENEFIT SHARING SCHEMES IN PROTECTING MOUNTAIN GORILLAS IN CENTRAL AFRICA

Presently, the mountain gorilla in Rwanda, Uganda, and the Democratic Republic of Congo is endangered mainly by poaching and habitat loss. This paper sets out to investigate the possible resolution of poaching involving the local community by using benefit sharing schemes with local communities. Using a bioeconomic model, the paper demonstrates that the current revenue sharing scheme yields suboptimal conservation outcomes. It is, however, shown that a performance‐linked benefit sharing scheme in which the Park Agency makes payment to the local community based on the growth of the gorilla stock can achieve socially optimal conservation. This scheme renders poaching effort by the local community, and therefore poaching fines and antipoaching enforcement toward the local community unnecessary. Given the huge financial outlay requirements for the ideal benefit sharing scheme, the Park Agencies in central Africa could reap more financial benefits for use in conservation if they employ an oligopolistic pricing strategy for gorilla tourism.     

Stochastic optimization for the ruin probability

The Cramér‐Lundberg insurance model is studied where the risk process can be controlled by reinsurance and by investment in a financial market. The performance criterion is the ruin probability. The problem can be imbedded in the framework of discrete‐time stochastic dynamic programming. Basic tools are the Howard improvement and the verification theorem. Explicit conditions are obtained for the optimality of employing no reinsurance and of not investing in the market.     

Time development of a Markov process in a finite population: Application to diffusion of information

A systematic procedure of truncating the hierarchy of moment equations describing the stochastic evolution of a Markov process in a finite population is developed. The procedure makes use of the asymptotic expression for a certain higher‐order moment of the relevant probability distribution and yields finite‐size corrections to all lower‐order moments. The usefulness of the method is illustrated by applying it to study the mean and the variance of the stochastic variable n(t), the number of active spreaders at time t, in Bartholomew's model of diffusion of information. The results thus obtained are compared with the ones following from the exact probability distribution for the model (wherever known) and the agreement between the two sets of results is found to be remarkably good.     

An extension of the Clark–Haussmann formula and applications

ABSTRACT

This work considers a financial market stochastic model where the uncertainty is driven by a multidimensional Brownian motion. The market price of the risk process makes the transition between real world probability measure and risk neutral probability measure. Traditionally, the martingale representation formulas under the risk neutral probability measure require the market price of risk process to be bounded. However, in several financial models the boundedness assumption of the market price of risk fails; for example a financial market model with the market price of risk following an Ornstein–Uhlenbeck process. This work extends the Clark–Haussmann representation formula to underlying stochastic processes which fail to satisfy the standard requirements. Our methodology is classical, and it uses a sequence of mollifiers. Our result can be applied to hedging and optimal investment in financial markets with unbounded market price of risk. In particular, the mean variance optimization problem can be addressed within our framework.     

Supply chain optimization of petroleum organization under uncertainty in market demands and prices

A multi-period stochastic planning model has been developed and implemented for a supply chain network of a petroleum organization operating in an oil producing country under uncertain market conditions. The proposed supply chain network consists of all activities related to crude oil production, processing and distribution. Uncertainties were introduced in market demands and prices. A deterministic optimization model was first developed and tested. The impact of uncertainty on the supply chain was studied by performing a sensitivity analysis in which ±20% deviations were introduced in market demands and prices of different commodities. A stochastic formulation was then proposed, which is based on the two-stage problem with finite number of realizations. The proposed stochastic programming approach proved to be quite effective in developing resilient production plans in light of high degree of uncertainty in market conditions. The anticipated production plans have a considerably lower expected value of perfect information (EVPI). The main conclusion of this study is that for an oil producing country with oil processing capabilities, the impact of economic uncertainties may be tolerated by an appropriate balance between crude exports and processing capacities.     

A class of two-sex branching processes with reproduction phase in a random environment

We model the demographic dynamics of populations with sexual reproduction where the reproduction phase occurs in a non-predictable environment and we assume the immigration/out-migration of mating units in the population. We introduce a general class of two-sex branching processes where, in each generation, the number of mating units which take part in the reproduction phase is randomly determined and the offspring probability distribution changes over time in a random environment. We provide several probabilistic results about the limit behaviour of populations whose dynamics is modelled by such a class of stochastic processes. In particular, we provide sufficient conditions for the almost sure extinction of the population or for its survival with a positive probability. As illustration, we include some simulated examples.     

A differential game model of a market of substitutable products

Modern industrial organization often classifies groups of differentiated products that are fairly good substitutes to belong to the same market. This paper develops a differential game model of a market of substitutable products. To avoid the problem of time-inconsistency, we solve a feedback Nash equilibrium solution for the game. A set of state-dependent equilibrium strategies is derived. Extensions of the model to a stochastic formulation and to an infinite time horizon specification are also provided.     

A discrete-time model of failure and repair

In this paper the authors introduce and study a model of failures and repairs of units with discrete lifetimes. They suppose that a unit has a sequence of tasks to perform and that its lifetime is measured by the number of tasks performed before its final, fatal failure. Upon a failure the unit may be repaired (with some probability) and then it may attempt again to perform the current task. The unit dies when (with some probability) a repair cannot be completed. We derive some stochastic comparisons of pairs of such models. The stochastic comparisons are then applied for obtaining results regarding the inheritance of several aging properties by the repaired unit. Various examples illustrate the applicability of the model. Some variants of the model of this paper can be viewed as discrete analogues of the notion of imperfect repair.     

The Further Study of Safety Stock under Uncertain Environment

Corresponding to stochastic variable, it is a better choice to describe the market demand uncertainty of innovative products with fuzzy variable because no historical data is available. Traditionally, possibility measure is regarded as the parallel concept of probability measure. However, it is, in fact, the credibility measure that plays the role of probability measure! Based on the credibility theory, this paper studies how to evaluate the safety stock of enterprise given desired product availability when the node enterprise market demand of supply chain is described by Gauss fuzzy variable. Thereinafter, the authors discuss the impact of required product availability and demand uncertainty on safety stock, compare the correlative issues with stochastic demand, and get some useful results.     

Modeling a stochastic multi-objective supplier quota allocation problem with price-dependent ordering

One of the interesting subjects in supply chain management is supply management, which generally relates to the activities regarding suppliers such as empowerment, evaluation, partnerships and so on. A major objective of supplier evaluation involves buyers determining the optimal quota allocated to each supplier when placing an order. In this paper, we propose a multi-objective model in which purchasing cost, rejected units, and late delivered units are minimized, while the obtained total score from the supplier evaluation process is maximized. We assume that the buyer obtains multiple products from a number of predetermined suppliers. The buyer faces a stochastic demand with a probability distribution of Poisson regarding each product type. A major assumption is that the supplier prices are linearly dependent on the order size of each product. Since demand is stochastic, the buyer may incur holding and stockout costs in addition to the regular purchasing cost. We use the well-known L-1 metric method to solve the supplier evaluation problem by utilizing two meta-heuristic algorithms to solve the corresponding mathematical problems.     

A logistics problem: a non-markovian queueing network model and algorithm

In this paper, a stochastic version of the classical deterministic balanced single commodity capacitated transportation network problem is presented. In this model, each arc of the network connects a supply node to a demand node and the flow of units forming along each arc of the network forms a stochastic process (i.e.G/M/1 queueing system with generally distributed interarrival time, a Markovian server, a single server, infinite capacity, and the first come first served queueing discipline). In this model, the total transportation cost is minimized such that the total supply rate is equal to the total demand rate, and the resulting probability of finding excessive congestion along each arc (i.e., the resulting probability of finding congestion inside the queueing system formed along each arc in excess of a fixed number) is equal to a desirable value     

赌博破产概率及其随机模拟试验

讨论了赌博问题中的最终破产概率,并给出了破产概率的随机模拟计算流程和一个具体例子的数值模拟结果.计算结果表明,由此方法得到破产概率的估计值与理论值的误差很小.最后,通过随机模拟给出游戏结束的平均次数.     

Mean–variance target-based optimisation for defined contribution pension schemes in a stochastic framework

We solve a mean–variance optimisation problem in the accumulation phase of a defined contribution pension scheme. In a general multi-asset financial market with stochastic investment opportunities and stochastic contributions, we provide the general forms for the efficient frontier, the optimal investment strategy, and the ruin probability. We show that the mean–variance approach is equivalent to a “user-friendly” target-based optimisation problem which minimises a quadratic loss function, and provide implementation guidelines for the selection of the target. We show that the ruin probability can be kept under control through the choice of the target level. We find closed-form solutions for the special case of stochastic interest rate following the Vasiček (1977) dynamics, contributions following a geometric Brownian motion, and market consisting of cash, one bond and one stock. Numerical applications report the behaviour over time of optimal strategies and non-negative constrained strategies.     

On-line Control Model for Cost-simulation Network Projects

This paper presents a newly developed hierarchical control model for several PERT type projects being realized simultaneously. The model has two objectives: to minimize the number of control points for an on-line control at the project level, and to maximize the probability that the slowest project can meet its due date on time (company level). On-line control is carried out separately for each project in order to minimize the number of control points subject to a chance constraint, which seeks to prevent deviation from the planned trajectory. If at the control point it is anticipated that the project will not be on target subject to the chance constraint, then an emergency is called. Under emergency conditions the company level is faced with the stochastic problem of budget reassigning among the projects enabling the faster projects to help the slower ones. A numerical example is presented.     

Modeling short‐term post‐offering price–volume relationships using Bayesian change‐point panel quantile regression

We propose a special panel quantile regression model with multiple stochastic change‐points to analyze latent structural breaks in the short‐term post‐offering price–volume relationships in China's growth enterprise market where the piecewise quantile equations are defined by change point indication functions. We also develop a new Bayesian inference and Markov chain Monte Carlo simulation approach to estimate the parameters, including the locations of change points, and put forth simulation‐based posterior Bayesian factor tests to find the best number of change points. Our empirical evidence suggests that the single change point effect is significant on quantile‐based price–volume relationships in China's growth enterprise market. The lagged initial public offering (IPO) return and the IPO volume rate of change have positive impacts on the current IPO return before and after the change point. Along with investors' gradually declining hot sentiment toward a new IPO, the market index volume rate of change induces the abnormal short‐term post‐offering IPO return to move back to the equilibrium. Copyright © 2015 John Wiley & Sons, Ltd.     

Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension

We consider two models for directed polymers in space‐time independent random media (the O'Connell‐Yor semidiscrete directed polymer and the continuum directed random polymer) at positive temperature and prove their KPZ universality via asymptotic analysis of exact Fredholm determinant formulas for the Laplace transform of their partition functions. In particular, we show that for large time τ, the probability distributions for the free energy fluctuations, when rescaled by τ^1/3, converges to the GUE Tracy‐Widom distribution. We also consider the effect of boundary perturbations to the quenched random media on the limiting free energy statistics. For the semidiscrete directed polymer, when the drifts of a finite number of the Brownian motions forming the quenched random media are critically tuned, the statistics are instead governed by the limiting Baik–Ben Arous–Péché distributions from spiked random matrix theory. For the continuum polymer, the boundary perturbations correspond to choosing the initial data for the stochastic heat equation from a particular class, and likewise for its logarithm—the Kardar‐Parisi‐Zhang equation. The Laplace transform formula we prove can be inverted to give the one‐point probability distribution of the solution to these stochastic PDEs for the class of initial data. © 2014 Wiley Periodicals, Inc.     

Default Times in a Continuous Time Markov Chain Economy

Abstract

A continuous time financial market is considered where randomness is modelled by a finite state Markov chain. Using the chain, a stochastic discount factor is defined. The probability distributions of default times are shown to be given by solutions of a system of coupled partial differential equations.     

联系概率的由来及其在风险决策中的应用

观察一简单随机摸球实验:当盒子中只有白球时,事件A="任抽一球是白球"是必然事件;当盒子中有白球黑球时,事件A是随机事件,这一实验表明事件A的随机性是2个事物(白、黑球)相互联系的一种属性,借此实验说明概率用联系数表述的原理以及联系概率的来由,同时还介绍了引出联系概率时用到的一些新概念,举例说明联系概率在风险决策中的应用.     

Solution sensitivity-based scenario reduction for stochastic unit commitment

A two-stage stochastic program is formulated for day-ahead commitment of thermal generating units to minimize total expected cost considering uncertainties in the day-ahead load and the availability of variable generation resources. Commitments of thermal units in the stochastic reliability unit commitment are viewed as first-stage decisions, and dispatch is relegated to the second stage. It is challenging to solve such a stochastic program if many scenarios are incorporated. A heuristic scenario reduction method termed forward selection in recourse clusters (FSRC), which selects scenarios based on their cost and reliability impacts, is presented to alleviate the computational burden. In instances down-sampled from data for an Independent System Operator in the US, FSRC results in more reliable commitment schedules having similar costs, compared to those from a scenario reduction method based on probability metrics. Moreover, in a rolling horizon study, FSRC preserves solution quality even if the reduction is substantial.     

Using Utility Functions to Model Risky Bonds

This paper prices defaultable bonds by incorporating inherent risks with the use of utility functions. By allowing risk preferences into the valuation of bonds, nonlinearity is introduced in their pricing. The utility‐function approach affords the advantage of yielding exact solutions to the risky bond pricing equation when familiar stochastic models are used for interest rates. This can be achieved even when the default probability parameter is itself a stochastic variable. Valuations are found for the power‐law and log utility functions under the interest‐rate dynamics of the extended Vasicek and CIR models.