Dynamic advertising and pricing with constant demand elasticities

In this paper we analyze a stochastic dynamic advertising and pricing model with isoelastic demand. The state space is discrete, time is continuous and the planing horizon is allowed to be finite or infinite. A dynamic version of the Dorfman–Steiner identity will be derived. Explicit expressions of the optimal advertising and pricing policies, of the value function and of the optimal advertising expenditures will be given. The general results will be used to analyze the case of impatient customers. Furthermore, particular time inhomogeneous models and homogeneous ones with and without discounting will be examined. We will study the social efficiency of a monopolist's optimal policies and the consequences of specific subsidies. From a buyer's perspective, our analysis reveals that waiting – when looking at (immediate) expected prices – is never profitable should two or more units be available. But we will also prove that the sequence of average sales prices is monotone decreasing. Moreover, the techniques applied to solve the discrete stochastic advertising and pricing problem will be used to solve a related deterministic control problem with continuous state space.     

指数风险偏好下的最优保险策略

本文讨论了当投保个体和保险公司为指数风险偏好时，在保费约束下投保个体的最优保险策略问题。本文采用求解对偶优化问题的方法求解这个问题，并给出当损失服从指数分布时最优保险策略解的解析式。本文最后讨论了投保个体和保险公司风险厌恶程度以及保费预算变化对个体最优保险策略的影响。     

Optimal portfolios and Heston's stochastic volatility model: an explicit solution for power utility

Given an investor maximizing utility from terminal wealth with respect to a power utility function, we present a verification result for portfolio problems with stochastic volatility. Applying this result, we solve the portfolio problem for Heston's stochastic volatility model. We find that only under a specific condition on the model parameters does the problem possess a unique solution leading to a partial equilibrium. Finally, it is demonstrated that the results critically hinge upon the specification of the market price of risk. We conclude that, in applications, one has to be very careful when exogenously specifying the form of the market price of risk.     

Making Good Decisions with Minimal Information: Simultaneous and Sequential Choice

The adaptive pressures facing humans and other animals to make decisions quickly can be met both by increasing internal information-processing speed and by minimizing the amount of information to be used. Here we focus on the latter effect and ask how, and how well, agents can make good decisions with a minimal amount of information, using two specific tasks as examples. When a choice must be made between simultaneously-available options, minimal information in the form of binary recognition (whether or not each item is recognized) can be used in the recognition heuristic to choose effectively. When options are encountered sequentially one at a time, minimal information as to whether or not each option is the best encountered so far is sufficient to guide agents using a simple search-cutoff rule to high performance along several choice criteria. Both of these examples have important economic as well as biological applications, and show the power of simple fast and frugal heuristics to produce good decisions with little information. This revised version was published online in August 2006 with corrections to the Cover Date.     

Optimal foreign debt for Egypt: A stochastic control approach

This study assesses the foreign debt policy in Egypt and contrasts it versus the optimal policy during the period 1985–2008. It also presents a forecast of the optimal debt during the period 2009–2014. The optimal debt policy was derived using an open economy model for Egypt. The uncertainties in the model stem from the uncertainties in the interest or debt service payments and the uncertainties in the rate of return on investments. The stochastic control approach was used to find the optimal debt policy. It was found that Egypt could borrow externally as long as the trend in the rate of return on investments exceeds the trend in the real interest rate or the trend in the rate of the debt service payments. The analysis finds that Egypt's foreign debt was higher than the optimal level before 1997. After 1997, foreign debt seems to converge to the optimal level. However, Egypt's foreign debt is still below its optimal level which results in an opportunity cost for the economy to grow, otherwise, GDP could have recorded a favorable increase.     

Energy balance climate models and general equilibrium optimal mitigation policies

In a general equilibrium model of the world economy, we develop a two-dimensional energy balance climate model featuring heat diffusion and anthropogenic forcing driven by global fossil fuel use across the sphere of the Earth. This introduces an endogenous location dependent temperature function, driving spatial characteristics, in terms of location dependent damages resulting from local temperature anomalies into the standard climate-economy framework. We solve the social planner's problem and characterize the competitive equilibrium for two polar cases differentiated by the degree of market integration. We define optimal taxes on fossil fuel use and how they may implement the planning solution. Our results suggest that if the implementation of international transfers across latitudes is not possible then optimal taxes are in general spatially non-homogeneous and may be lower at poorer latitudes. The degree of spatial differentiation of optimal taxes depends on heat transportation. By employing the properties of the spatial model, we show by numerical simulations how the impact of thermal transport across latitudes on welfare can be studied.     

Optimal dividend policy and growth option

We analyse the interaction between the dividend policy and the decision on investment in a growth opportunity of a liquidity constrained firm. This leads us to study a mixed singular control/optimal stopping problem for a diffusion that we solve quasi-explicitly by establishing a connection with an optimal stopping problem. We characterize situations where it is optimal to postpone the distribution of dividends in order to invest at a subsequent date in the growth opportunity. We show that uncertainty and liquidity shocks have an ambiguous effect on the investment decision.      

A comment on the role of prices for excludable public goods

Blomquist and Christensen [(2005). The role of prices for excludable public goods, International Tax and Public Finance, 12 ,61–79] argue that welfare is initially decreasing in the price of an excludable public good and that the case for a positive price for an excludable public good price is weak. We argue that this result follows from their particular characterization of the public good and that an alternative and equally reasonable characterization overturns their result. Hence, the policy case for a positive price on the public good is stronger than Blomquist and Christiansen suggest. JEL Classification H21 · H41     

An Analysis of the Out-of-Market Gap for DVDs in the U.S.

We examine the out-of-market gap – the time between the end of a film’s theatrical run and its release on DVD – for a sample of U.S. films during 1988-2005. The average gap declined from 58.14 days in 1998 to 27.93 days in 2005; by 2005, 39% of the films were released on DVD prior to leaving the theaters. Probit and hazard models are estimated to explore the factors that influence a distributor’s decision to release a film on DVD before it exits the theaters, and the timing of the release for films that appear on DVD after they leave the theaters.