An optimal-incentive contract for managers with exponential utility

This paper examines the manager–investor relationship in the case of exponential utility when the manager of investments in real or financial assets has an endowment which can be invested in the risky assets for which he has private information. We obtain a relationship showing trade-offs or hedging behavior among the investments the manager can choose for himself and the principal. Even with the hedging ability of the manager, the well-known first-best solution with ‘no moral hazard’ risk-sharing is obtained among these possible solutions to the manager's problem by specifying a ‘no conflict of interest’, zero investment by the manager of his own endowment in those risky assets for which he has private information. Thus, the agent imputes no disutility to the assignment of the principal's investments and the investor is assured of an investment strategy that he would make if he had access to the manager's private information.     

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 tests and estimators for truncated exponential families

Blackwell-Rao-Lehmann-Scheffe' theory is used to derive the minimum variance unbiased estimators for the functions of scale and truncation parameters as well as the reliability function of the truncated exponential family distribution. Uniformly most powerful unbiased tests of hypotheses are formulated. Finally, a particular model of this family, viz., the truncated exponential model is discussed.     

Turnpike property and convergence rate for an investment model with general utility functions

In this paper we aim to address two questions faced by a long-term investor with a power-type utility at high levels of wealth: one is whether the turnpike property still holds for a general utility that is not necessarily differentiable or strictly concave, the other is whether the error and the convergence rate of the turnpike property can be estimated. We give positive answers to both questions. To achieve these results, we first show that there is a classical solution to the HJB equation and give a representation of the solution in terms of the dual function of the solution to the dual HJB equation. We demonstrate the usefulness of that representation with some nontrivial examples that would be difficult to solve with the trial and error method. We then combine the dual method and the partial differential equation method to give a direct proof to the turnpike property and to estimate the error and the convergence rate of the optimal policy when the utility function is continuously differentiable and strictly concave. We finally relax the conditions of the utility function and provide some sufficient conditions that guarantee the turnpike property and the convergence rate in terms of both primal and dual utility functions.     

Optimal investment and reinsurance policies for an insurer with ambiguity aversion

In this paper, we study the optimal investment and reinsurance problem for an insurer based on the variance premium principle, in which three cases are considered. First, we assume that the financial market does not exist. The insurer only holds an insurance business, and the optimal reinsurance problem is studied. Subsequently, we assume that there exists a financial market with an accurately modeled risky asset. The optimal investment and reinsurance problem is investigated under these conditions. Finally, we consider the general case in which the insurer is concerned about the model ambiguity of both the insurance market and the financial market. In all three cases, the value function is set to maximize the expected utility of terminal wealth. By employing the dynamic programming principle, we derive the Hamilton–Jacobi–Bellman (HJB) equations, which are satisfied by the value functions and obtain closed-form solutions for optimal reinsurance and investment policies and the value functions in all three cases. Most interestingly, we elucidate how investment improves the insurer’s utility and find that the existence of ambiguity can significantly affect the optimal policies and value functions. We also compare the ambiguities in the two markets and find that ambiguity in the insurance market has much more significant impact on the value function than the ambiguity in the financial market. It implies that it is more valuable for insurer to precisely evaluate the insurance risk. We also provide some numerical examples and economic explanations to illustrate our results.     

Optimal investment with vintage capital: Equilibrium distributions

The paper concerns the study of equilibrium points, or steady states, of economic systems arising in modeling optimal investment with vintage capital, namely, systems where all key variables (capitals, investments, prices) are indexed not only by time but also by age. Capital accumulation is hence described as a partial differential equation (briefly, PDE), and equilibrium points are in fact equilibrium distributions in the variable of ages. A general method is developed to compute and study equilibrium points of a wide range of infinite dimensional, infinite horizon, optimal control problems. We apply the method to optimal investment with vintage capital, for a variety of data, deriving existence and uniqueness of equilibrium distribution, as well as analytic formulas for optimal controls and trajectories in the long run. The examples suggest that the same method can be applied to other economic problems displaying heterogeneity. This shows how effective the theoretical machinery of optimal control in infinite dimension is in computing explicitly equilibrium distributions. To this extent, the results of this work constitute a first crucial step towards a thorough understanding of the behavior of optimal paths in the long run.     

Optimal investment with taxes: an existence result

We study the deterministic control problem of maximizing utility from consumption of an agent who seeks to optimally allocate his wealth between consumption and investment in a financial asset subject to taxes on benefits with first-in–first-out priority rule on sales. Short sales are prohibited and consumption is restricted to be non-negative. Such a problem has been introduced in a previous paper by the same authors where the first-order conditions have been derived. In this paper, we establish an existence result for this non-classical optimal control problem.     

Optimal investment of variance-swaps in jump-diffusion market with regime-switching

We consider a general jump-diffusion market with regime-switching where the jump risk is modeled as a Markov-modulated Poisson random measure. In this incomplete market, we price the variance-swaps using a combination of the Esscher transform and change of measure on time-inhomogeneous Markov chains. We study the dynamic optimal investment problem of the variance-swaps and characterize the optimal feedback strategy. Moreover, a closed-form solution to the HJB PDE associated with the stochastic control problem is established and the verification theorem is proved. The numerical analysis based on a two-state Markov chain uncovers some robust features of the optimal investment strategy.     

Optimal R&D investment for a risk-averse entrepreneur

Entrepreneurs investing in R&D projects face technical uncertainty associated with the cost to completion of the project, which is idiosyncratic and inherently unhedgeable. We extend existing real options models of R&D investment to incorporate the cost of bearing this unhedgeable risk and find it decreases risk-averse entrepreneurs’ valuations of R&D projects and increases the minimum NPVs required for continued investment in R&D (threshold NPVs) relative to ‘unpriced risk’ values and threshold NPVs. As in the ‘unpriced risk’ case, for less risk-averse entrepreneurs with small R&D projects, threshold NPVs remain negative and decrease with technical uncertainty. However, for sufficiently risk-averse entrepreneurs with sufficiently large R&D projects, threshold NPVs can become positive and increase with technical uncertainty.     

Optimal production and portfolio investment decisions

This paper takes a further step towards the integration of the theories of production and finance under uncertainty. It sets up a continuous time-diffusion process model of production by firms and portfolio investment by individuals and provides a simultaneous solution to these two decisions. The derived equilibrium conditions, being in the stockholders' interest, are specific in form, and are determined by two factors: attitudes of investors towards risk and the systematic risks of the firm.     

Optimal investment models with vintage capital: Dynamic programming approach

The dynamic programming approach for a family of optimal investment models with vintage capital is here developed. The problem falls into the class of infinite horizon optimal control problems of PDE’s with age structure that have been studied in various papers (12, 11, 33 and 35) either in cases when explicit solutions can be found or using Maximum Principle techniques.     

Optimal consumption and portfolio rules with intertemporally dependent utility of consumption

In the usual consumption portfolio problem, lifetime utility is assumed to be time-additive. This assumption has been criticized for failing to capture important intertemporal dependencies in utility such as intertemporal risk aversion and habit formation. This paper studies the consumption portfolio problem for a class of intertemporally dependent utility functions.     

Optimal investment decisions when time-horizon is uncertain

Many investors do not know with certainty when their portfolio will be liquidated. Should their portfolio selection be influenced by the uncertainty of exit time? In order to answer this question, we consider a suitable extension of the familiar optimal investment problem of Merton [Merton, R.C., 1971. Optimal consumption and portfolio rules in a continuous-time model. Journal of Economic Theory 3, 373–413], where we allow the conditional distribution function of an agent’s time-horizon to be stochastic and correlated to returns on risky securities. In contrast to existing literature, which has focused on an independent time-horizon, we show that the portfolio decision is affected.     

Optimal consumption and investment under partial information

We consider a stock market model where prices satisfy a stochastic differential equation with a stochastic drift process. The investor’s objective is to maximize the expected utility of consumption and terminal wealth under partial information; the latter meaning that investment decisions are based on the knowledge of the stock prices only. We derive explicit representations of optimal consumption and trading strategies using Malliavin calculus. The results apply to both classical models for the drift process, a mean reverting Ornstein-Uhlenbeck process and a continuous time Markov chain. The model can be transformed to a complete market model with full information. This allows to use results on optimization under convex constraints which are used in the numerical part for the implementation of more stable strategies. Supported by the Austrian Science Fund FWF, project P17947-N12. We thank two anonymous referees for their comments which led to a considerable improvement of the paper.     

Optimal investment policy of the regulated firm

The main purpose of this paper is to investigate the optimal investment behaviour of a regulated firm and to show that the Averch-Johnson effect of overcapitalization does not necessarily occur in a dynamic model under the assumption of concave revenue function. There may be three cases of undercapitalization, overcapitalization, and neutralization. As the result, whether the Averch-Johnson effect appears or not is crucially dependent on the regulated rate of return and the firm's planning horizon.     

Optimal automobile emission control: A household utility model

Traditionally, benefit-cost studies value mortality changes using equivalent capital approaches. That is, the social benefit of decreased mortality is related to an increased income stream. A utility model which accounts for mortality changes as changes in individual or household risks is proposed, it is then employed to analyze automotive emission control. The utility model selects optimal national emission control levels for individual households by maximizing a combination of risk and consumption. The social optimum is taken as the median levels of all households. The control levels for three pollutants are more stringent than those calculated by a more typical benefit-cost method but less strict than the present statutory standards.

The data has been taken for several sources. The risk data is from an epidemiology study that associates age specific mortality rates with various factors including pollution levels. Economic benefits are derived from several estimates of the association of pollution with vegetation and material damages and soiling. Automobile control costs are from EPA and auto company estimates.     

Optimal consumption and investment under time-varying relative risk aversion

We consider the continuous time consumption-investment problem originally formalized and solved by Merton in case of constant relative risk aversion. We present a complete solution for the case where relative risk aversion with respect to consumption varies with time, having in mind an investor with age-dependent risk aversion. This provides a new motivation for life-cycle investment rules. We study the optimal consumption and investment rules, in particular in the case where the relative risk aversion with respect to consumption is increasing with age.     

我国城市基础设施外资利用的政策建议

文章论述了我国城市基础设施建设中外资利用现状及存在问题 ,提出了相关的政策建议。     

The harvest strategy: how to implement a disaster for the environment and the stockholders

This paper examines the harvest strategy – an often recommended approach for dealing with a weak business unit. It is shown to be a strategy that intertwines the distinct levels of strategy making with the ultimate goal of increasing corporate value. However, in order to be successful it must be carried out inconspicuously. Inconspicuousness is a euphemism for deception in the case of the harvest strategy. Such behavior, when an industrial accident occurs, exposes shareholders to the risk of substantial losses if the accident happens in high-risk technology industries. The authors illustrate their contention by analysing the financial consequences of the Union Carbide tragedy at Bhopal and the Exxon disaster at Valdez. © 1998 John Wiley & Sons, Ltd and ERP Environment.