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Compound Poisson Process (compound + poisson_process)
Selected AbstractsEarnings-Based Bonus CompensationFINANCIAL REVIEW, Issue 4 2009António Câmara G39; M52 Abstract This article studies the cost of contingent earnings-based bonus compensation. We assume that the firm has normal and abnormal earnings. The normal earnings result from normal firm activities and are modeled as an arithmetic Brownian motion. The abnormal earnings result from surprising activities (e.g., introduction of an unexpected new product, an unexpected strike) and are modeled as a compound Poisson process where the earnings jump sizes have a normal distribution. We investigate, in a simple general equilibrium model, how normal and abnormal earnings affect the cost of contingent bonus compensation to the firm. [source] Variability of shallow overland flow velocity and soil aggregate transport observed with digital videographyHYDROLOGICAL PROCESSES, Issue 20 2008A. Sidorchuk Abstract Field experiments at Tiramoana station 30 km north of Christchurch, New Zealand using an erosion plot 16·5 m long, 0·6 m wide, and with a slope of 14,14·5° on rendzina soil aimed to measure the variability of flow velocity and of soil aggregates transport rate in shallow overland flow. Discharge/cross-section area ratio was used to estimate mean velocity, and high-speed digital video camera and image analysis provided information about flow and sediment transport variability. Six flow runs with 0·5,3·0 L s,1 discharges were supercritical with Froude numbers close to or more than 1. Mean flow velocity followed Poiseuille law, float numbers were more than 1·5 and hydraulic resistance was an inverse proportional function of the Reynolds number, which is typical for laminar flows. Hence actual velocity varied through time significantly and the power spectrum was of ,red-noise', which is typical for turbulent flow. Sediment transport rates had even higher variability, and soil aggregates transport was a compound Poisson process. Copyright © 2008 John Wiley & Sons, Ltd. [source] OPTIMAL CONTINUOUS-TIME HEDGING WITH LEPTOKURTIC RETURNSMATHEMATICAL FINANCE, Issue 2 2007We examine the behavior of optimal mean,variance hedging strategies at high rebalancing frequencies in a model where stock prices follow a discretely sampled exponential Lévy process and one hedges a European call option to maturity. Using elementary methods we show that all the attributes of a discretely rebalanced optimal hedge, i.e., the mean value, the hedge ratio, and the expected squared hedging error, converge pointwise in the state space as the rebalancing interval goes to zero. The limiting formulae represent 1-D and 2-D generalized Fourier transforms, which can be evaluated much faster than backward recursion schemes, with the same degree of accuracy. In the special case of a compound Poisson process we demonstrate that the convergence results hold true if instead of using an infinitely divisible distribution from the outset one models log returns by multinomial approximations thereof. This result represents an important extension of Cox, Ross, and Rubinstein to markets with leptokurtic returns. [source] STOCK LEVELS AND DELIVERY RATES IN VENDORMANAGED INVENTORY PROGRAMSPRODUCTION AND OPERATIONS MANAGEMENT, Issue 1 2001BEN A. CHAOUCH Using the latest information technology, powerful retailers like Wal-Mart have taken the lead in forging shorter replenishment-cycles, automated supply systems with suppliers. With the objective to reduce cost, these retailers are directing suppliers to take full responsibility for managing stocks and deliveries. Suppliers' performance is measured according to how often inventory is shipped to the retailer, and how often customers are unable to purchase the product because it is out of stock. This emerging trend also implies that suppliers are absorbing a large part of the inventory and delivery costs and, therefore, must plan delivery programs including delivery frequency to ensure that the inherent costs are minimized. With the idea to incorporate this shift in focus, this paper looks at the problem facing the supplier who wants quicker replenishment at lower cost. In particular, we present a model that seeks the best trade-off among inventory investment, delivery rates, and permitting shortages to occur, given some random demand pattern for the product. The process generating demand consists of two components: one is deterministic and the other is random. The random part is assumed to follow a compound Poisson process. Furthermore, we assume that the supplier may fail to meet uniform shipping schedules, and, therefore, uncertainty is present in delivery times. The solution to this transportationinventory problem requires determining jointly delivery rates and stock levels that will minimize transportation, inventory, and shortage costs. Several numerical results are presented to give a feel of the optimal policy's general behavior. [source] Pricing and hedging of quanto range accrual notes under Gaussian HJM with cross-currency Levy processesTHE JOURNAL OF FUTURES MARKETS, Issue 10 2009Szu-Lang Liao This study analyzes the pricing and hedging problems for quanto range accrual notes (RANs) under the Heath-Jarrow-Morton (HJM) framework with Levy processes for instantaneous domestic and foreign forward interest rates. We consider the effects of jump risk on both interest rates and exchange rates in the pricing of the notes. We first derive the pricing formula for quanto double interest rate digital options and quanto contingent payoff options; then we apply the method proposed by Turnbull (Journal of Derivatives, 1995, 3, 92,101) to replicate the quanto RAN by a combination of the quanto double interest rate digital options and the quanto contingent payoff options. Using the pricing formulas derived in this study, we obtain the hedging position for each issue of quanto RANs. In addition, by simulation and assuming the jump risk to follow a compound Poisson process, we further analyze the effects of jump risk and exchange rate risk on the coupons receivable in holding a RAN. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:973,998, 2009 [source] The compound Poisson process perturbed by a diffusion with a threshold dividend strategyAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 1 2009Kam C. Yuen Abstract In this paper, we consider the compound Poisson process perturbed by a diffusion in the presence of the so-called threshold dividend strategy. Within this framework, we prove the twice continuous differentiability of the expected discounted value of all dividends until ruin. We also derive integro-differential equations for the expected discounted value of all dividends until ruin and obtain explicit expressions for the solution to the equations. Along the same line, we establish explicit expressions for the Laplace transform of the time of ruin and the Laplace transform of the aggregate dividends until ruin. In the case of exponential claims, some examples are provided. Copyright © 2008 John Wiley & Sons, Ltd. [source] |