增长期权对最优资本结构的影响研究：企业生命周期的视角

资产构成和生命周期的动态关系决定了企业最优资本结构的变化趋势。本文在利息税盾和破产成本的权衡理论框架下,运用实物期权方法,理论上揭示了增长期权动态执行导致最优资本结构随企业生命周期的变化规律,扩展分析了股东-债权人代理冲突对最优资本结构的影响,并提供了基于中国沪深A股上市公司的经验证据。结果表明：随着企业由年轻走向成熟,增长期权不断执行和在位资产逐渐累积会降低企业总体的破产风险,从而企业最优财务杠杆呈现上升趋势且增长速度逐渐放缓;股东和债权人在增长期权执行决策上的代理冲突导致的投资不足会降低最优财务杠杆,但代理成本随企业生命周期推进呈递减趋势。     

On a Risk Model with Surplus-dependent Premium and Tax Rates

In this paper, the compound Poisson risk model with surplus-dependent premium rate is analyzed in the taxation system proposed by Albrecher and Hipp (Bl?tter der DGVFM 28(1):13–28, 2007). In the compound Poisson risk model, Albrecher and Hipp (Bl?tter der DGVFM 28(1):13–28, 2007) showed that a simple relationship between the ruin probabilities in the risk model with and without tax exists. This so-called tax identity was later generalized to a surplus-dependent tax rate by Albrecher et al. (Insur Math Econ 44(2):304–306, 2009). The present paper further generalizes these results to the Gerber–Shiu function with a generalized penalty function involving the maximum surplus prior to ruin. We show that this generalized Gerber–Shiu function in the risk model with tax is closely related to the ‘original’ Gerber–Shiu function in the risk model without tax defined in a dividend barrier framework. The moments of the discounted tax payments before ruin and the optimal threshold level for the tax authority to start collecting tax payments are also examined.     

A Note on the Suboptimality of Path-Dependent Pay-Offs in Lévy Markets

Abstract

Cox and Leland used techniques from the field of stochastic control theory to show that, in the particular case of a Brownian motion for the asset log-returns, risk-averse decision makers with a fixed investment horizon prefer path-independent pay-offs over path-dependent pay-offs. In this note we provide a novel and simple proof for the Cox and Leland result and we will extend it to general Lévy markets where pricing is based on the Esscher transform (exponential tilting). It is also shown that, in these markets, optimal path-independent pay-offs are increasing with the underlying final asset value. We provide examples that allow explicit verification of our theoretical findings and also show that the inefficiency cost of path-dependent pay-offs can be significant. Our results indicate that path-dependent investment pay-offs, the use of which is widespread in financial markets, do not offer good value from the investor's point of view.     

Approximate Hedging of Contingent Claims under Transaction Costs for General Pay-offs

Abstract

In 1985 Leland suggested an approach to price contingent claims under proportional transaction costs. Its main idea is to use the classical Black–Scholes formula with a suitably enlarged volatility for a periodically revised portfolio whose terminal value approximates the pay-off h(S _?T )?=?(S _?T ???K)⁺ of the call option. In subsequent studies, Lott, Kabanov and Safarian, and Gamys and Kabanov provided a rigorous mathematical analysis and established that the hedging portfolio approximates this pay-off in the case where the transaction costs decrease to zero as the number of revisions tends to infinity. The arguments used heavily the explicit expressions given by the Black–Scholes formula leaving open the problem whether the Leland approach holds for more general options and other types of price processes. In this paper we show that for a large class of the pay-off functions Leland's method can be successfully applied. On the other hand, if the pay-off function h(x) is not convex, then this method does not work.     

基于ZZ杠杆模型的资本结构影响因素研究——来自中国制造业上市公司的经验证据

ZZ杠杆模型理论上解决"定量求解最优资本结构"这一财务领域长期难以解决的问题,由于该模型建立在一系列理想假设之上,有待实证的进一步检验.基于ZZ杠杆模型研究了资本结构的影响因素,从沪市A股制造业上市公司中筛选了200家符合条件的公司为样本,选用其2008年的横截面财务数据进行实证检验.结果表明,ZZ杠杆模型中的变量是显著影响我国上市公司资本结构的因素:即公司价值波动率与资本结构负相关,所得税税率及平均债务期限与资本结构正相关.结论证实了ZZ杠杆模型在中国市场总体上是成立的.     

政府投资环保的随机增长模型

本文分析了一个带有污染的随机内生增长模型.利用随机最优化的方法,求出了最优的政府环保投资比率和最优的税收政策.并进一步得出了最优的收入税因污染的外部性指标、生产的扰动的增大而减少;而最优消费税则因这两个参数的增大而增加的结论.     

The Tax Identity For Markov Additive Risk Processes

Taxed risk processes, i.e. processes which change their drift when reaching new maxima, represent a certain type of generalizations of Lévy and of Markov additive processes (MAP), since the times at which their Markovian mechanism changes are allowed to depend on the current position. In this paper we study generalizations of the tax identity of Albrecher and Hipp (2007) from the classical risk model to more general risk processes driven by spectrally-negative MAPs. We use the Sparre Andersen risk processes with phase-type interarrivals to illustrate the ideas in their simplest form.     

The influence of corporate taxes on pricing and capital structure in property-liability insurance

A change in the corporate tax level can have a significant impact on rate making and capital structure for insurance companies. The purpose of this paper is to study this effect on competitive equity-premium combinations for different asset and liability models while retaining a fixed safety level. This is a crucial consideration as a change in the tax rate leads, in general, to a different risk of insolvency. Hence, fixing the safety level serves to isolate the effect of taxes without shifting the insurer’s risk situation whenever taxes are varied. The model framework includes stochastic assets as well as stochastic claims costs. We further compare the results for liability models with and without a jump component. Insurance rate making is conducted using option pricing theory.     

OPTIMAL HARVESTING AND SPATIAL PATTERNS IN A SEMIARID VEGETATION SYSTEM

We consider an infinite time horizon spatially distributed optimal harvesting problem for a vegetation and soil water reaction diffusion system, with rainfall as the main external parameter. By Pontryagin's maximum principle, we derive the associated four‐component canonical system (CS), and numerically analyze this and hence the optimal control problem in two steps. First, we numerically compute a rather rich bifurcation structure of flat (spatially homogeneous) canonical steady states and patterned canonical steady states (FCSS and PCSS, respectively), in 1D and 2D. Then, we compute time‐dependent solutions of the CS that connect to some FCSS or PCSS. The method is efficient in dealing with nonunique canonical steady states, and thus also with multiple local maxima of the objective function. It turns out that over wide parameter regimes the FCSS, i.e., spatially uniform harvesting, are not optimal. Instead, controlling the system to a PCSS yields a higher profit. Moreover, compared to (a simple model of) private optimization, the social control gives a higher yield, and vegetation survives for much lower rainfall. In addition, the computation of the optimal (social) control gives an optimal tax to incorporate into the private optimization.     

多期动态背景下的债务共谋与产品市场竞争关系模型研究

利用超博弈理论分析方法建立了多期动态背景下的债务共谋与产品市场竞争关系模型并进行了分析。发现在战略替代下，一个产业中公司之间相互竞争程度越高，则维持零负债共谋战略所需要的折现系数就越大，产业竞争程度较高的公司偏离零负债共谋的可能性越大。因此，债务共谋结论重新加强了竞争程度与最优杠杆正相关的观点。     

具有跳扩散模型下永久公司债券的定价和最佳资产结构

综合运用偏微分方程方法和结构化方法,在公司资产价值演化服从跳扩散模型下,研究永久公司债券的定价问题和最佳资产结构问题,获得了公司债券,股东权益和公司总价值的定价表达式和最佳杠杆比率的表达式.     

On the exponential process associated with a CARMA-type process

We study the correlation decay and the expected maximal increments of the exponential processes determined by continuous-time autoregressive moving average (CARMA)-type processes of order (p, q). We consider two background driving processes, namely fractional Brownian motions and Lévy processes with exponential moments. The results presented in this paper are significant extensions of those very recent works on the Ornstein–Uhlenbeck-type case (p = 1, q = 0), and we develop more refined techniques to meet the general (p, q). In the concluding section, we discuss the perspective role of exponential CARMA-type processes in stochastic modelling of the burst phenomena in telecommunications and the leverage effect in financial econometrics.     

On taxed spectrally negative Lévy processes with draw-down stopping

In this paper we consider a spectrally negative Lévy risk model with tax. With the ruin time replaced by a draw-down time with a linear draw-down function and for a constant tax rate, we find expressions for the present values of tax payments. They generalize previous results in Albrecher et al. (2008). Alternative proofs are given for the special case of Cramér–Lundberg risk models. Optimal barrier taxation policies are discussed.     

具有相依理赔量的离散时间风险模型的破产问题

本文研究了理赔量具有一阶自回归结构以及在此条件下引入折现率和双险种两种广义离散时间金融风险模型的破产问题.利用数学递推的方法,获得了破产持续时间分布和盈余首次穿过给定水平x的时刻分布所满足的积分方程,并给出当理赔量服从指数分布时相关破产分布的数值分析结果,推广了经典离散时间金融风险模型的结构和破产问题.     

Environmental tax policy,habit formation and nonlinear dynamics

In this paper, we study the impact of environmental tax policy on the dynamic property in an environment-growth model (John and Pecchenino 1994) [3]. We assume that the government levies consumption tax and uses the tax revenue to improve environmental quality. We show that the economic dynamics can be represented by a first-order difference equation in environmental quality when there is no habit formation of environmental quality. If agents have habit formation of environmental quality, the economic dynamics will be represented by a second-order difference equation in environmental quality. In both cases, chaotic and cyclical fluctuations may exist if agents’ preference towards environmental quality, the maintenance efficiency relative to degradation and the tax rate are sufficiently low. However, the economy undergoes transformation from complex dynamics to simple dynamics as the tax rate increases. Furthermore, in the presence of habit formation of environmental quality, an increase in the degree of habit formation lowers the possibility of complex dynamics.     

“公司+农户”型订单农业供应链的政府税收补贴机制

基于“公司+农户”型订单农业背景,引入“随行就市,保底收购”的合约价格方式并考虑农产品流通中的数量损耗,探究了政府向公司征税并将税收收入补贴给农户对于订单农业供应链决策及运作的影响。首先,在政府对农户的补贴系数外生时,以政府征税不补贴为基准模型,对比分析了政府征税不补贴和征税补贴两种情形下的均衡结果,发现:若公司对农产品深加工,则进项税率小于销项税率,政府对农户进行税收补贴,可激励农户提高生产量并促使公司降低保底价格,进而增加双方期望收益,即征税补贴是征税不补贴的帕累托改善;若公司对农产品初加工,进项税率等于销项税率,则税收补贴带来的收益全部被公司利用其强势地位所攫取,单纯的税收补贴难以实现农户增产增收的目的。随后,在政府补贴系数内生时,证明了深加工情形下存在唯一最优的税收补贴系数使得政府社会福利最大化,且最优的税收补贴系数随各参数的变化存在上下界。最后,引入数值算例验证了上述结论,同时发现,深加工情形下政府决策的最优税收补贴系数随流通损耗率的增加而减小,随销项税率和供应链边际利润率的增大而增大;社会福利和公司的期望收益对流通损耗率的变化较之农户的期望收益对其变化更为敏感。     

On the on-line rent-or-buy problem in probabilistic environments

Fujiwara and Iwama [In: The 13th Annual International Symposium on Algorithms and Computation, pp. 476–488 (2002)] first integrated probability distribution into the classical competitive analysis to study the rental problem. They assumed that the future inputs are drawn from an exponential distribution, and obtained the optimal competitive strategy and the competitive ratio by the derivative method. In this paper, we introduce the interest rate and tax rate into the continuous model of Fujiwra and Iwama [In: The 13th Annual International Symposium on Algorithms and Computation, pp. 476–488 (2002)]. Moreover, we use the forward difference method in different probabilistic environments to consider discrete leasing models both with and without the interest rate. We not only give the optimal competitive strategies and their competitive ratios in theory, but also give numerical results. We find that with the introduction of the interest rate and tax rate, the uncertainty involved in the process of decision making will diminish and the optimal purchasing date will be put off.     

The distribution of tax payments in a Lévy insurance risk model with a surplus-dependent taxation structure

We study the distribution of tax payments in the model of Kyprianou and Zhou [Kyprianou, A.E., Zhou, X., 2009. General tax structures and the Lévy insurance risk model. J. Appl. Probab. (in press)], that is a Lévy insurance risk model with a surplus-dependent tax rate. More precisely, after a short discussion on the so-called tax identity, we derive a recursive formula for arbitrary moments of the discounted tax payments until ruin and we identify the distribution of the tax payments when there is no force of interest.     

On the n-Coupling Problem

In this paper we obtain based on an idea of M. Knott and C. S. Smith (1994, Linear Algebra Appl.199, 363–371) characterizations of solutions of three-coupling problems by reduction to the construction of optimal couplings of each of the variables to the sum. In the case of normal distributions this leads to a complete solution. Under a technical condition this idea also works for general distributions and one obtains explicit results. We extend these results to the n-coupling problem and derive a characterization of optimal n-couplings by several 2-coupling problems. This leads to some constructive existence results for Monge solutions.