结合逃税的最优税收理论研究评述

最优税收理论主要研究税制的最优设计问题,而逃税理论主要致力于政府的最优执行问题,最近出现了将这两种理论结合起来的研究趋势。结合逃税的最优税收理论,包括最优所得税和最优商品税等内容,研究结果表明:结合逃税的最优税收理论并不能得出比标准最优税收理论更为明确的政策结论,其还有待于进一步的研究和发展。     

On optimal stratifications for multivariate distributions

Summary

In the present paper we study the problem of optimal stratifications for estimating the mean vector y of a given multivariate distribution F(x) with covariance matrix ζ both in cases of proportionate and of optimal (or generalized Neyman) allocations. It is noted that an “optimal stratification” is meant for one to make the covariance matrix of an unbiased estimator X for μ minimal, in the sense of semi-order defined below, in the symmetric matrix space. We show the existence of an optimal stratification and the necessary conditions for a stratification to be optimal. Besides we prove that an optimal stratification can be represented by a “hyperplane stratification” or a “quadratic hypersurface stratification” according to the proportionate or optimal (or generalized Neyman) allocation, and that the set of all optimal (or admissible) stratifications is a minimal complete class in the analogous sense of decision theory. Further we discuss the optimal stratification when a criterion based on a suitable real-valued function is adopted instead of the semi-order.     

突发事件风险下考虑企业社会责任的闭环供应链决策

基于突发事件风险概率小、后果大的特点,考虑企业社会责任的闭环供应链应对突发事件风险中再制造成本扰动风险的优化决策。结果表明：当再制造成本扰动较小时,不需要调整闭环供应链的生产计划,反之则需要调整生产计划;若再制造成本扰动值增大,则需提高最优零售价并减少最优产量;若再制造成本扰动量绝对值增大,则需降低最优零售价格并增加最优产量。关注CSR的水平越高,最优的批发价格和最优的零售价反而会降低。最优的回收利用率、最优的产量及整个链条的总利润与CSR水平呈正相关。若再制造成本扰动值较小,零售商回收模式更加合适,而若扰动值超过一定值则应该选择制造商回收模式。     

Robustly optimal monetary policy in a microfounded New Keynesian model

We consider optimal monetary stabilization policy in a New Keynesian model with explicit microfoundations, when the central bank recognizes that private-sector expectations need not be precisely model-consistent, and wishes to choose a policy that will be as good as possible in the case of any beliefs close enough to model-consistency. We show how to characterize robustly optimal policy without restricting consideration a priori to a particular parametric family of candidate policy rules. We show that robustly optimal policy can be implemented through commitment to a target criterion involving only the paths of inflation and a suitably defined output gap, but that a concern for robustness requires greater resistance to surprise increases in inflation than would be considered optimal if one could count on the private sector to have “rational expectations.”     

On the Interaction of Real and Financial Decisions of the Firm Under Uncertainty

This study analyzes the interaction between the optimal level of investment and debt financing. For this purpose, a model is structured in which a firm, facing an uncertain price, has to decide on its optimal level of investment and debt. The amount of investment sets a limit on output whose optimal level is determined after price is realized. The debt involved is risky (there exists a possibility of bankruptcy). The analysis proves that investment and its optimal financing have to be simultaneously determined and that a negative relationship exists between operating and financial leverage. We also demonstrate that as the tax rate increases, optimal capacity decreases and optimal leverage increases. An analysis of the impact of changes in the expected price shows that under some conditions, an increase in expected price would lead to an increase in optimal investment (firm size) and a decrease in optimal debt.     

Real income growth and optimal credit use

Borrowing may be optimal if real income is expected to increase. If income growth is uncertain, optimal credit use is not obvious. A two period model of consumption for determining optimal credit use is presented. The impact of real income growth is analyzed with numerical analysis. The results may be useful for financial counselors and educators, as well as for insight into empirical patterns of credit use. The income growth rate expected by the household plays a crucial role in determining optimal credit use for current consumption.     

Taxation, Migration, and Pollution

This paper analyzes optimal fiscal, environmental and immigration policy for a single jurisdiction. In the presence of immigration quotas, taxes on the output of externality-producing industries should be higher than indicated by the standard rule for Pigovian corrective taxation. Immigration quotas are not optimal if fiscal instruments can be used to control immigration, and relaxation of immigration quotas generally increases domestic welfare. If optimal taxes are imposed on immigrants, no immigration quota should be imposed, and a version of the traditional Pigovian rule characterizes optimal taxation of domestic externalities. If production in the immigrants' country of origin causes trans-boundary spillovers, domestic welfare can be improved by lighter taxation of immigrants or by further relaxation of immigration quotas. This revised version was published online in July 2006 with corrections to the Cover Date.     

Optimal fiscal and monetary policy in an economy without capital

This paper is concerned with the structure and time-consistency of optimal fiscal and monetary policy in an economy without capital. In a dynamic context, optimal taxation means distributing tax distortions over time in a welfare-maximizing way. For a barter economy, our main finding is that with debt commitments of sufficiently rich maturity structure, an optimal policy, if one exists, is time-consistent. In a monetary economy, the idea of optimal taxation must be broadened to include an ‘inflation tax’, and we find that time-consistency does not carry over. An optimal ‘inflation tax’ requires commitment by ‘rules’ in a sense that has no counterpart in the dynamic theory of ordinary excise taxes. The reason time-consistency fails in a monetary economy is that nominal assets should, from a welfare-maximizing point of view, always be taxed away via an immediate inflation in a kind of ‘capital levy’. This emerges as a new possibility when money is introduced into an economy without capital.     

Reinsuring Climatic Risk Using Optimally Designed Weather Bonds

The aim of this paper is to determine the optimal structure of a weather bond, i.e. a bond whose coupons depend on the occurence of a weather event. The stress is put more on the structuration than on the simple pricing of the bond. Therefore, instead of looking only at the bond issue, we consider it as a part of a more general transaction, involving three agents: a firm, which wants to be hedged against its weather risk, an investor, which buys the bond and a bank, which has an intermediary key role. Then, we derive the optimal characteristics of the whole transaction. But the bond structure which is obtained, corresponds to a minimal structure: indeed, only the bond optimal price function and its optimal reimbursement level (amount which is paid back when an event occurs) can be determined while there is a degree of freedom in the choice of the optimal coupon. Therefore, this indeterminacy may be interpreted as a marketing tool and it could play an important role in the negotiation process between the issuer and the investor.     

The optimal rate of inflation revisited

Inflation viewed as a tax on cash balances is investigated using the optimal commodity tax framework. The optimal inflation rate is shown to depend on the effect of changes in the rate of inflation on quantity demanded of ‘costly-to-produce’ goods. Even when other goods are taxed, it is not always optimal to have a positive tax on money, as Phelps and others have claimed. A zero tax or even a rate of deflation greater than the pre-tax rate of interest may be optimal.     

Optimal life insurance with no-borrowing constraints: duality approach and example

We solve an optimal portfolio choice problem under a no-borrowing assumption. A duality approach is applied to study a family’s optimal consumption, optimal portfolio choice, and optimal life insurance purchase when the family receives labor income that may be terminated due to the wage earner’s premature death or retirement. We establish the existence of an optimal solution to the optimization problem theoretically by the duality approach and we provide an explicitly solved example with numerical illustration. Our results illustrate that the no-borrowing constraints do not always impact the family’s optimal decisions on consumption, portfolio choice, and life insurance. When the constraints are binding, there must exist a wealth depletion time (WDT) prior to the retirement date, and the constraints indeed reduce the optimal consumption and the life insurance purchase at the beginning of time. However, the optimal consumption under the constraints will become larger than that without the constraints at some time later than the WDT.     

Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities

We derive the optimal investment policy of a risk-averse investorin a market where there is a textbook arbitrage opportunity,but where liabilities must be secured by collateral. We findthat it is often optimal to underinvest in the arbitrage bytaking a smaller position than collateral constraints allow.Even when the optimal policy is followed, the arbitrage portfoliotypically experiences losses before the final convergence date.In fact, its initial performance may be indistinguishable fromthat of a conventional portfolio with a poor track record. Theseresults have important implications for the role of arbitrageursin financial markets.     

Optimal portfolio choice in the bond market

We consider the Merton problem of optimal portfolio choice when the traded instruments are the set of zero-coupon bonds. Working within a Markovian Heath–Jarrow–Morton model of the interest rate term structure driven by an infinite-dimensional Wiener process, we give sufficient conditions for the existence and uniqueness of an optimal trading strategy. When there is uniqueness, we provide a characterization of the optimal portfolio as a sum of mutual funds. Furthermore, we show that a Gauss–Markov random field model proposed by Kennedy [Math. Financ. 4, 247–258(1994)] can be treated in this framework, and explicitly calculate the optimal portfolio. We show that the optimal portfolio in this case can be identified with the discontinuities of a certain function of the market parameters.     

Stochastic dominance and portfolio analysis

The principle of stochastic dominance is used to characterize the optimal efficient sets when the distributions of the random prospects belong to a family. Most of the well-known distributions are considered. In each case, the optimal efficient sets are characterized by easily verifiable conditions on the parameters of the distributions. These optimal efficient sets are then compared with the corresponding mean-variance (MV) efficient set. It is often found that the optimal efficient sets are proper subsets of the MV efficient set. Thus, the MV criterion is a proper efficiency criterion, but the MV efficient set can be excessively large compared to the optimal efficient set.     

Optimal monetary growth with accommodating fiscal policy in a small open economy

This paper emphasizes how the choice of the optimal monetary growth rate in a small open economy under perfect capital mobility depends upon the accommodating policy chosen to maintain the overall budget constraint in the economy. When this occurs through lump sum taxation, the optimal monetary growth rate is shown to be the ‘distorted’ Friedman monetary rule. If the adjustment occurs through the income tax rate, the optimal monetary growth rate involves a Phelps-type tradeoff between the income tax rate and the inflation tax rate. The framework is suited for analyzing optimal macroeconomic policy in general and the latter part of the paper considers an optimal monetary-fiscal package.     

Learning about Predictability: The Effects of Parameter Uncertainty on Dynamic Asset Allocation

This paper examines the effects of uncertainty about the stock return predictability on optimal dynamic portfolio choice in a continuous time setting for a long-horizon investor. Uncertainty about the predictive relation affects the optimal portfolio choice through dynamic learning, and leads to a state-dependent relation between the optimal portfolio choice and the investment horizon. There is substantial market timing in the optimal hedge demands, which is caused by stochastic covariance between stock return and dynamic learning. The opportunity cost of ignoring predictability or learning is found to be quite substantial.     

Around the Life Cycle: Deterministic Consumption-Investment Strategies

We study a classical continuous-time consumption-investment problem of a power utility investor with deterministic labor income with the important feature that the consumption-investment process is constrained to be deterministic. This is motivated by the design of modern pension schemes of defined contribution type where, typically, the savings rate is constant and the proportional investment in growth stocks is a function of age or time-to-retirement, a so-called life-cycle investment strategy. We derive and study the optimal behavior corresponding to the optimal product design within this realistic family of products with deterministic decision profiles. We also propose a couple of suboptimal deterministic strategies inspired from the optimal stochastic strategy and compare the optimal stochastic control, the optimal deterministic control, and these suboptimal deterministic controls. The conclusion is that only little is lost by constraining to deterministic strategies and only little is lost by implementing the suboptimal simple explicit strategies rather than the optimal one we derive.     

Optimal Reinsurance Under the Risk-Adjusted Value of an Insurer’s Liability and an Economic Reinsurance Premium Principle

In this article, an optimal reinsurance problem is formulated from the perspective of an insurer, with the objective of minimizing the risk-adjusted value of its liability where the valuation is carried out by a cost-of-capital approach and the capital at risk is calculated by either the value-at-risk (VaR) or conditional value-at-risk (CVaR). In our reinsurance arrangement, we also assume that both insurer and reinsurer are obligated to pay more for a larger realization of loss as a way of reducing ex post moral hazard. A key contribution of this article is to expand the research on optimal reinsurance by deriving explicit optimal reinsurance solutions under an economic premium principle. It is a rather general class of premium principles that includes many weighted premium principles as special cases. The advantage of adopting such a premium principle is that the resulting reinsurance premium depends not only on the risk ceded but also on a market economic factor that reflects the market environment or the risk the reinsurer is facing. This feature appears to be more consistent with the reinsurance market. We show that the optimal reinsurance policies are piecewise linear under both VaR and CVaR risk measures. While the structures of optimal reinsurance solutions are the same for both risk measures, we also formally show that there are some significant differences, particularly on the managing tail risk. Because of the integration of the market factor (via the reinsurance pricing) into the optimal reinsurance model, some new insights on the optimal reinsurance design could be gleaned, which would otherwise be impossible for many of the existing models. For example, the market factor has a nontrivial effect on the optimal reinsurance, which is greatly influenced by the changes of the joint distribution of the market factor and the loss. Finally, under an additional assumption that the market factor and the loss have a copula with quadratic sections, we demonstrate that the optimal reinsurance policies admit relatively simple forms to foster the applicability of our theoretical results, and a numerical example is presented to further highlight our results.     

Properties of Optimal Smooth Functions in Additive Models for Hedging Multivariate Derivatives

In this paper, we consider an optimal hedging problem for multivariate derivative based on the additive sum of smooth functions on individual assets that minimize the mean square error (or the variance with zero expected value) from the derivative payoff. By applying the necessary and sufficient condition with suitable discretization, we derive a set of linear equations to construct optimal smooth functions, where we show that the computations involving conditional expectations for the multivariate derivatives may be reduced to those of unconditional expectations, and thus, the total procedure can be executed efficiently. We investigate the theoretical properties for the optimal smooth functions and clarify the following three facts: (i) the value of each individual option takes an optimal trajectory to minimize the mean square hedging error under the risk neutral probability measure, (ii) optimal smooth functions for the put option may be constructed using those for the call option (and vice versa), and (iii) delta in the replicating portfolio may be computed efficiently. Numerical experiments are included to show the effectiveness of our proposed methodology.     

American capped call options on dividend-paying assets

This article addresses the problem of valuing American calloptions with caps on dividend-paying assets. Since early exerciseis allowed, the valuation problem requires the determinationof optimal exercise policies. Options with two types of capsare analyzed: constant caps and caps with a constant growthrate. For constant caps, it is optimal to exercise at the firsttime at which the underlying asset's price equals or exceedsthe minimum of the cap and the optimal exercise boundary forthe corresponding uncapped option. For caps that grow at a constantrate, the optimal exercise strategy can be specified by threeendogenous parameters.