Mortality risk modeling: Applications to insurance securitization

This paper proposes a stochastic mortality model featuring both permanent longevity jump and temporary mortality jump processes. A trend reduction component describes unexpected mortality improvement over an extended period of time. The model also captures the uneven effect of mortality events on different ages and the correlations among them. The model will be useful in analyzing future mortality dependent cash flows of life insurance portfolios, annuity portfolios, and portfolios of mortality derivatives. We show how to apply the model to analyze and price a longevity security.     

The utility of cash flow forecasts in the management of corporate cash balances

This paper considers the stochastic cash balance problem. A dynamic simple policy (DSP) is proposed to minimise transaction costs, under a general cost structure, when the cash flows are not independently or identically distributed. The validity of the approach is demonstrated using the scenario of double exponentially distributed cash flows considered by Penttinen. A data set from a large multinational is used to demonstrate the practical application of the DSP. To provide conditional expectations of future cash flows, a time series model is developed to provide forecasts.     

考虑需求率变化与延期支付的临时订货模型

供应商给予临时价格折扣、并针对采购商的临时订货给予优惠的延期支付条件;同时考虑到采购商的自身需求即为终端需求并对价格敏感,由于考虑需求量变化的同时考虑到时间因素,因此需求率实际上发生了改变。在这样的背景下,采购商在价格变化时刻面临两种选择:以低价购进大量货物或者放弃这个机会。本文以EOQ模型单位产品成本为参考,从成本节约最大的角度出发,分析了采购商临时订货量的确定过程,并用数例分析了参数变化对最优订货以及成本节约情况的影响。     

Performance of the heuristic procedures for constrained projects with progress payments

All large scale resource constrained projects involve cash flows occurring during their life cycle. Several recent studies consider the problem of scheduling projects to maximise the net present value (NPV) of these cash flows. Their basic common assumption is that cash flows are mainly associated with specific events and they occur at event realisation times. An alternative assumption, which can be more realistic, is that cash inflows occur periodically, for example every month, as progress payments. This article considers the problem of maximising NPV given the alternative assumption. Three different heuristic rules are developed. The performance of these heuristic rules is analysed through a full factorial experiment with 108 scheduling conditions. The results indicate that three rules provide near-optimal schedules with respect to NPV maximisation while producing time schedules that do not delay the project completion time extensively.     

Dynamic lot-sizing with price changes and price-dependent holding costs

This paper proposes a new formulation of the dynamic lot-sizing problem with price changes which considers the unit inventory holding costs in a period as a function of the procurement decisions made in previous periods. In Section 1, the problem is defined and some of its fundamental properties are identified. A dynamic programming approach is developed to solve it when solutions are restricted to sequential extreme flows, and results from location theory are used to derive an O(T²) algorithm which provides a provably optimal solution of an integer linear programming formulation of the general problem. In Section 2, a heuristic is developed for the case where the inventory carrying rates and the order costs are constant, and where the item price can change once during the planning horizon. Permanent price increases, permanent price decreases and temporary price reductions are considered. In Section 3, extensive testing of the various optimal and heuristic algorithms is reported. Our results show that, in this context, the two following intuitive actions usually lead to near optimal solutions: accumulate stock at the lower price just prior to price increase and cut short on orders when a price decrease is imminent.     

Analysis of the stochastic cash balance problem using a level crossing technique

The simple cash management problem includes the following considerations: the opportunity cost of holding too much cash versus the penalty cost of not having enough cash to meet current needs; the cost incurred (or profit generated) when making changes to cash levels by increasing or decreasing them when necessary; the uncertainty in timing and magnitude of cash receipts and cash disbursements; and the type of control policy that should be used to minimize the required level of cash balances and related costs. In this paper, we study a version of this problem in which cash receipts and cash disbursements occur according to two independent compound Poisson processes. The cash balance is monitored continuously and an order-point, order-up-to-level, and keep-level \( \left( {s, S, M} \right) \) policy is used to monitor the content, where \( s \le S \le M \). That is, (a) if, at any time, the cash level is below s, an order is immediately placed to raise the level to S; (b) if the cash level is between s and M, no action is taken; (c) if the cash level is greater than M, the amount in excess of M is placed into an earning asset. We seek to minimize the expected total costs per unit time of running the cash balance. We use a level-crossing approach to develop a solution procedure for finding the optimal policy parameters and costs. Several numerical examples are given to illustrate the tradeoffs.     

Dynamic pricing of inventory/capacity with infrequent price changes

We consider a problem of dynamically pricing a single product sold by a monopolist over a short time period. If demand characteristics change throughout the period, it becomes attractive for the company to adjust price continuously to respond to such changes (i.e., price-discriminate intertemporally). However, in practice there is typically a limit on the number of times the price can be adjusted due to the high costs associated with frequent price changes. If that is the case, instead of a continuous pricing rule the company might want to establish a piece-wise constant pricing policy in order to limit the number of price adjustments. Such a pricing policy, which involves optimal choice of prices and timing of price changes, is the focus of this paper.We analyze the pricing problem with a limited number of price changes in a dynamic, deterministic environment in which demand depends on the current price and time, and there is a capacity/inventory constraint that may be set optimally ahead of the selling season. The arrival rate can evolve in time arbitrarily, allowing us to model situations in which prices decrease, increase, or neither. We consider several plausible scenarios where pricing and/or timing of price changes are endogenized. Various notions of complementarity (single-crossing property, supermodularity and total positivity) are explored to derive structural results: conditions sufficient for the uniqueness of the solution and the monotonicity of prices throughout the sales period. Furthermore, we characterize the impact of the capacity constraint on the optimal prices and the timing of price changes and provide several other comparative statics results. Additional insights are obtained directly from the solutions of various special cases.     

A Decision Analysis Approach to Cash Flow Management

We propose a method of applying the Hespos and Strassmann "stochastic decision tree" framework, originally intended for investment decisions, to cash flow management. Sequences of uncertain events, such as a strike, affecting forecast cash flows are represented by a probability tree. Forecasts of constituent cash flows such as sales and costs are represented by Beta distributions dependent on paths through the tree. Monte Carlo simulations sample these distributions, and equations provided in the model convert the sampled cash flows to cash balances in each period. Frequencies of cash balances weighted by probabilities along paths through the tree yield a combined relative frequency distribution of cash balances for each period. These and related results may be used by management to plan financing arrangements to meet cash requirements in the future.     

Valuation under technological change

This paper presents a valuation model, which includes the possibility of a future change in technology that affects in the short term the level of net cash flows receivable. The user can consider the effects of such a change on the flows, depending on whether the company is an innovator itself, or a follower of the innovations of others. The model is based upon a number of assumptions. The cash flows before the technological breakthrough follow a geometric Brownian motion. The breakthrough is modelled by a Poisson jump. For the innovator, cash flows are boosted, then decline through competition. By contrast, for the technological follower the breakthrough has an immediate depressing effect on cash flows, but subsequent cash flows rise and are modelled by an upward logistic curve.     

The impact of dynamic pricing on the economic order decision

This paper analyzes the impact of dynamic pricing on the single product economic order decision of a monopolist retailer. Items are procured from an external supplier according to the economic order quantity (EOQ) model and are sold to customers on a single market without competition following the simple monopolist pricing problem. Coordinated decision making of optimal pricing and ordering is influenced by operating costs – including ordering and inventory holding costs – and the demand rate obtained from a price response function. The retailer is allowed to vary the selling price, either in a fixed number of discrete points in time or continuously. While constant and continuous pricing have received much attention in the literature, problems with a limited number of price changes are rather rare. This paper illustrates the benefit of dynamically changing prices to achieve operational efficiency in the EOQ model, that is to trigger high demand rates when inventories are high. We provide structural properties of the optimal time instants when the price should be changed. Taking into account costs for changes in price, it provides numerical guidance on number, timing, and size of price changes during an order cycle. Numerical examples show that the benefits of dynamic pricing in an EOQ framework can be achieved with only a few price changes and that products being unprofitable under static pricing may become profitable under dynamic pricing.     

Lot Sizes for One-Time-Only Sales

The order quantity which minimizes discounted cash flows for a one-time-only sale is determined. Current inventory may be at or exceed the usual reorder point when the sale is consummated. In the latter case, the company may decide to buy nothing, especially if a large minimum order quantity is required in order to obtain the price discount. The same model can also be used to handle the case of an impending price increase. Exact and approximate solutions are presented which recommend the order quantity, the associated cost savings, minimum acceptable percentage price discount and minimum vendor quantity requirements.     

Project Scheduling with Discounted Cash Flows and Progress Payments

In all large scale projects, there correspond cash flows that incur throughout the life of the project. The scheduling of these projects to maximize the present value of the cash flows has been a topic of recent research. The basic assumption of earlier research is that the cash flows are mainly associated with some events of the project and they occur at the event realization times. However, in several real life projects, the cash inflows do not occur at the event realization times, rather they occur at the end of some time periods, like months, as progress payments. In this article, maximizing the present value of the cash flows in such projects is considered and a mixed-integer formulation of the problem is presented. In this formulation, activity profit curves are defined and used. Computational experience on some randomly generated test problems provides promising results especially when the Benders Decomposition technique is employed for solving the problem.     

Trade Credit and the Economic Order Quantity—A Further Extension

This paper extends the various contributions that have been made in this area, and in particular addresses the following issues: (i) why trade credit is granted, and the effect on the basic model where it is with-drawn; (ii) the legitimacy of certain assumptions in the various models which have been put forward to date; (iii) the interaction of other stockholding costs, such as storage and deterioration costs, with trade credit; (iv) the implications for stockholding where a business can sell goods acquired on credit for cash before the suppliers have to be paid and the order lead-time is less than the credit period. The paper also reviews whether trade credit should be included in the weighted cost of capital, and whether the holding-cost function should include interest received on the sale price, rather than cost.     

Can properly discounted projects follow geometric Brownian motion?

The geometric Brownian motion is routinely used as a dynamic model of underlying project value in real option analysis, perhaps for reasons of analytic tractability. By characterizing a stochastic state variable of future cash flows, this paper considers how transformations between a state variable and cash flows are related to project volatility and drift, and specifies necessary and sufficient conditions for project volatility and drift to be time-varying, a topic that is important for real option analysis because project value and its fluctuation can only seldom be estimated from data. This study also shows how fixed costs can cause project volatility to be mean-reverting. We conclude that the conditions of geometric Brownian motion can only rarely be met, and therefore real option analysis should be based on models of cash flow factors rather than a direct model of project value.     

基于国际估值准则的A股定价实证分析

尽管金融学理论认为股票的价值是未来无限期预期现金流的一个贴现,但针对国际股市的实证结果显示,股票实际价格很大程度上取决于市场对其未来一两年内的盈利预期等中期基本面因素.近3年里,A股创造的世界罕见的大起大落,引起了社会各界对A股定价是否合理的广泛争论.为此,我们设计了一个相对估值模型,根据国际股市的定价规则来给A股定价.实证结果显示,A股已经从2007年的估值泡沫回落到2008年的合理估值水平.还可以经过进一步地扩展模型讨论单个股票的定价问题.最后,讨论了实证结果的引申含义和一些政策建议.     

Optimal access pricing for natural monopoly networks when costs are sunk and revenues are uncertain

This paper studies optimal access pricing for natural monopoly networks with large sunk costs and uncertain revenues. Using techniques from the option pricing literature, we show that the optimal access price corresponds to a risk-free form of the Efficiency Component Pricing Rule (ECPR), that is, where the opportunity cost is based on the risk free rate of return. We also show that at levels of revenue above the optimal level that triggers entry, the entrant should pay a premium above risk-free ECPR that rewards the incumbent for relinquishing his rights to the risky cash flows at the higher revenue level.     

A sample-path approach to optimal position liquidation

We consider the problem of optimal position liquidation where the expected cash flow stream due to transactions is maximized in the presence of temporary or permanent market impact. A stochastic programming approach is used to construct trading strategies that differentiate decisions with respect to the observed market conditions, and can accommodate various types of trading constraints. As a scenario model, we use a collection of sample paths representing possible future realizations of state variable processes (price, trading volume etc.), and employ a heuristical technique of sample-path grouping, which can be viewed as a generalization of the standard nonanticipativity constraints.     

Estimation of mean and variance of net present value with certain and uncertain project life: a multiperiod CAPM approach

A multiperiod capital asset pricing model has the ability to consider risk by incorporating correlation between project and market parameters. This paper presents expressions for mean and variance of net present value of a project, in a multiperiod capital asset pricing model context, for the cases of certain and uncertain project lives. Both cases consider two types of cash flows, independent and correlated over time. The effects of (i) uncertainty in project life, (ii) correlation amongst subsequent cash flows, and (iii) the elasticity of expectations on the estimates of mean and variance of net present value have been studied through a numerical example.     

Cash management cost reduction using data mining to forecast cash demand and LP to optimize resources

This paper presents a two step model aimed at reducing cash management costs in a bank’s branch. First, data mining was used to forecast daily cash demand, comparing an ARMA-ARCH model with a neural network. Secondly, using the prior result, a linear programming model was solved. The optimal allocation of resources, i.e., cash collections and supplies was estimated showing that the model can be a helpful tool to support the determination of collections and supplies at the bank branch.     

Convex upper and lower bounds for present value functions

In this paper we present an efficient methodology for approximating the distribution function of the net present value of a series of cash‐flows, when discounting is presented by a stochastic differential equation as in the Vasicek model and in the Ho–Lee model. Upper and lower bounds in convexity order are obtained. The high accuracy of the method is illustrated for cash‐flows for which no analytical results are available. Copyright © 2001 John Wiley & Sons, Ltd.