Merton's portfolio optimization problem in a Black and Scholes market with non-Gaussian stochastic volatility of Ornstein-Uhlenbeck type

We study Merton's classical portfolio optimization problem for an investor who can trade in a risk-free bond and a stock. The goal of the investor is to allocate money so that her expected utility from terminal wealth is maximized. The special feature of the problem studied in this paper is the inclusion of stochastic volatility in the dynamics of the risky asset. The model we use is driven by a superposition of non-Gaussian Ornstein-Uhlenbeck processes and it was recently proposed and intensively investigated for real market data by Barndorff-Nielsen and Shephard (2001) . Using the dynamic programming method, explicit trading strategies and expressions for the value function via Feynman-Kac formulas are derived and verified for power utilities. Some numerical examples are also presented.     

NEWS-GENERATED DEPENDENCE AND OPTIMAL PORTFOLIOS FOR n STOCKS IN A MARKET OF BARNDORFF-NIELSEN AND SHEPHARD TYPE

We consider Merton's portfolio optimization problem in a Black and Scholes market with non-Gaussian stochastic volatility of Ornstein–Uhlenbeck type. The investor can trade in n stocks and a risk-free bond. We assume that the dependence between stocks lies in that they partly share the Ornstein–Uhlenbeck processes of the volatility. We refer to these as news processes, and interpret this as that dependence between stocks lies solely in their reactions to the same news. The model is primarily intended for assets that are dependent, but not too dependent, such as stocks from different branches of industry. We show that this dependence generates covariance, and give statistical methods for both the fitting and verification of the model to data. Using dynamic programming, we derive and verify explicit trading strategies and Feynman–Kac representations of the value function for power utility.     

Pricing by Arbitrage Under Arbitrary Information

A substantial applications literature on pricing by arbitrage has effectively restricted information to that arising solely from securities markets; return distributions are then governed solely by past prices. We reconsider pricing by arbitrage in markets rendered incomplete by arbitrary information, which, moreover, may influence required returns. We show that contingent claims depending solely on securities' normalized price histories are priced by arbitrage if and only if all risk-adjusted probabilities agree upon the law of primitive securities' normalized prices. We show how existing diffusion-based results can be preserved, and resolve an issue relating to Merton's (1973) stochastic interest rate model.     

An intertemporal capital asset pricing model under heterogeneous beliefs

An intertemporal CAMP under heterogeneous beliefs is derived. It is shown that an asset's risk consists of three components: the market consensus of volatility risk, the market consensus of the risk induced by changes in the investment opportunity set, and risk associated with uncertain shifts in investor's subjective expectations. The multiperiod market price of risk with heterogeneous beliefs defines a new structure of market risk that captures contemporaneous changes in investors' subjective expectations and the dynamics of the investment opportunity set. The investors' demand for risky assets also is examined under heterogeneous belief. In addition, the model derived provides a generalized version of other CAPM's, such as the classical CAPM, Merton's intertemporal CAPM, and Bredeen's consumption-based CAPM.     

SIMULATION-BASED PORTFOLIO OPTIMIZATION FOR LARGE PORTFOLIOS WITH TRANSACTION COSTS

We consider a portfolio optimization problem where the investor's objective is to maximize the long-term expected growth rate, in the presence of proportional transaction costs. This problem belongs to the class of stochastic control problems with singular controls , which are usually solved by computing solutions to related partial differential equations called the free-boundary Hamilton–Jacobi–Bellman (HJB) equations . The dimensionality of the HJB equals the number of stocks in the portfolio. The runtime of existing solution methods grow super-exponentially with dimension, making them unsuitable to compute optimal solutions to portfolio optimization problems with even four stocks. In this work we first present a boundary update procedure that converts the free boundary problem into a sequence of fixed boundary problems. Then by combining simulation with the boundary update procedure, we provide a computational scheme whose runtime, as shown by the numerical tests, scales polynomially in dimension. The results are compared and corroborated against existing methods that scale super-exponentially in dimension. The method presented herein enables the first ever computational solution to free-boundary problems in dimensions greater than three.     

A COMPLETE THEORY OF COMPARATIVE STATICS FOR DIFFERENTIABLE OPTIMIZATION PROBLEMS

A new comparative statics formalism using generalized compensated derivatives is presented that, in contrast to existing methodologies, directly yields constraint‐free semidefiniteness results for any differentiable, constrained optimization problem. The formalism provides a natural and powerful method of constructing comparative statics results, free of constraints and unrestricted in scope. New results on envelope relations, invariance conditions, rank inequalities and non‐uniqueness are derived that greatly extend their utility and reach. The methodology is illustrated by deriving the comparative statics of multiple linear constraint utility maximization models and the principal‐agent problem with hidden actions, both highly nontrivial and hitherto unsolved problems.     

TD-LTE-A上行信道估计中基于加权的插值算法

TD-LTE-A上行信道估计中的线性插值算法只利用数据两端的两个导频位置的信道响应进行插值,不能很好拟合信道响应。针对此问题,提出了基于加权平均的插值算法。该算法以线性插值算法为基础,首先利用连续3个导频位置的信道响应进行线性插值得到数据位置的两个初步插值结果,再在此基础上引入权值α,最后对初步插值结果进行加权得到数据位置的信道响应。在EPA环境下的MATLAB仿真结果表明,相对于线性插值算法,基于加权的插值算法在不过度增加计算复杂度的情况下能降低系统的误比特率。     

Pricing Discrete European Barrier Options Using Lattice Random Walks

This paper designs a numerical procedure to price discrete European barrier options in Black-Scholes model. The pricing problem is divided into a series of initial value problems, one for each monitoring time. Each initial value problem is solved by replacing the driving Brownian motion by a lattice random walk. Some results from the theory of Besov spaces show that the convergence rate of lattice methods for initial value problems depends on two factors, namely the smoothness of the initial value (or the value function) and the moments for the increments of the lattice random walk. This fact is used to obtain an efficient method to price discrete European barrier options. Numerical examples and comparisons with other methods are carried out to show that the proposed method yields fast and accurate results.     

Causes of nonlinearities in low-order models of the real exchange rate

This paper investigates the extent to which modern DSGE models, which feature local currency pricing, home bias, nontraded goods, and incomplete markets, can generate nonlinear real exchange rate dynamics that are consistent with those found in the time series literature using data from the current floating period. Our key findings are as follows. First, if the true model can be appropriately characterized as a set of linear equations, then linearity tests that utilize univariate autoregressions of the real exchange rate suffer from an omitted variables problem, which leads them to overestimate the true incidence of nonlinearity. Consequently, studies that fail to control for this problem may spuriously find evidence of nonlinearities in the data, despite the fact that the data generating process may be linear. Second, we propose a strategy that can largely eliminate this distortion. Finally, we find that DSGE models solved using higher order approximations are capable of generating true structural nonlinearities in real exchange rates both asymptotically and in short samples.     

Monopoly, Pareto and Ramsey Mark-ups

Monopoly prices are too high. It is a price level problem, in the sense that the relative mark-ups have Ramsey optimal proportions, at least for independent constant elasticity demands. I show that this feature of monopoly prices breaks down the moment one demand is replaced by the textbook linear demand or, even within the constant elasticity framework, dependence is introduced. The analysis provides a single Generalized Inverse Elasticity Rule for the problems of monopoly, Pareto and Ramsey.      

A METHOD FOR PRICING AMERICAN OPTIONS USING SEMI‐INFINITE LINEAR PROGRAMMING

We introduce a new approach for the numerical pricing of American options. The main idea is to choose a finite number of suitable excessive functions (randomly) and to find the smallest majorant of the gain function in the span of these functions. The resulting problem is a linear semi‐infinite programming problem, that can be solved using standard algorithms. This leads to good upper bounds for the original problem. For our algorithms no discretization of space and time and no simulation is necessary. Furthermore it is applicable even for high‐dimensional problems. The algorithm provides an approximation of the value not only for one starting point, but for the complete value function on the continuation set, so that the optimal exercise region and, for example, the Greeks can be calculated. We apply the algorithm to (one‐ and) multidimensional diffusions and show it to be fast and accurate.     

基于干扰抑制的恒模波束跟踪新算法

当干扰信号强度不小于期望信号时,常规恒模算法（CMA）会错误跟踪到干扰信号;期望信 号导向矢量线性约束恒模算法（LSCCMA）通过对期望信号来波方向约束,可正确跟踪到期望 信号,但是算法在干扰信号来波方向上不能形成明显的零陷。为此,提出了基于干扰约束的 恒模算法（LICCMBTA）。理论分析和仿真结果证明,该算法不仅可以正确跟踪到期望信号, 并且可实现在多个强干扰信号来波方向上形成深度可调的干扰零陷,从而提高了常规恒模算 法波束跟踪的稳健性。     

SENSITIVITY ANALYSIS OF NONLINEAR BEHAVIOR WITH DISTORTED PROBABILITY

In this paper, we propose a sensitivity‐based analysis to study the nonlinear behavior under nonexpected utility with probability distortions (or “distorted utility” for short). We first discover the “monolinearity” of distorted utility, which means that after properly changing the underlying probability measure, distorted utility becomes locally linear in probabilities, and the derivative of distorted utility is simply an expectation of the sample path derivative under the new measure. From the monolinearity property, simulation algorithms for estimating the derivative of distorted utility can be developed, leading to gradient‐based search algorithms for the optimum of distorted utility. We then apply the sensitivity‐based approach to the portfolio selection problem under distorted utility with complete and incomplete markets. For the complete markets case, the first‐order condition is derived and optimal wealth deduced. For the incomplete markets case, a dual characterization of optimal policies is provided; a solvable incomplete market example with unhedgeable interest rate risk is also presented. We expect this sensitivity‐based approach to be generally applicable to optimization problems involving probability distortions.     

一种基于主动学习的中文新词识别算法

分词是中文自然语言处理的重要基础，新词的不断涌现是分词的最大难题。针对新词识别定义不清、语料缺乏的实际问题，提出了一种以大规模神经网络预训练模型为基础，并结合主动学习和人工规则的新词识别算法。利用预训练模型高效识别候选新词，使用基于不确定性和代表性样本选择的主动学习策略辅助标注新词，利用热度规则、突发性规则和合成性规则识别和过滤新词发现结果。针对新词识别评价标准不一致的问题，给出了一般性准确率和受限制准确率两条规范测试指标。与现有最优算法进行实验对比，所提算法两项指标分别提高了16%和4%。     

A Negotiation-Oriented Model of Auditor-Client Relationships

The increasing frequency and complexity of inter-organizational relationships suggests that inter-organizational negotiations should represent an area of increasing concern to management and academicians. Unfortunately, there is little theorizing about, nor study of, these negotiations. The few extant models are heavily influenced by models of individual negotiating styles that are then raised to the inter-organizational level with minimal change. The model developed here attempts to provide a framework for understanding the context of these inter-organizational negotiations by identifying and illuminating factors that influence the outcome of interactions in various long-term supplier relationships. Factors discussed include dynamic and stable environments, organizational cultures, role involvement, previous interactions between the individuals and organizations, and the unique characteristics of the decision-making processes that characterize the specific parties. As a framework for our presentation, we draw upon Kleinman and Palmon's (1999) theory of audit firm-client firm relationships, which is based on Kahn et al.'s (1964) Role Episode Model and Merton's (1966) Role Set Model. This paper incorporates Shakun's (1988) theory of evolutionary system design. The inclusion of the latter improves upon Kleinman and Palmon's work by first providing a better motive for the interaction between the parties, and second by shedding further light on the dynamics of the negotiation process.     

Use of two-limit probit regression model : An analysis of lender response to loan requests

Research problems where the observed dependent variable is restricted to lie within an interval with massing of some of the observations at the limiting values of the interval are frequent in business research studies. This paper analyzes one such problem—that of lender response to a business loan application. The unique features of a regression model with a doubly limited dependent variable are explained and interpreted. Parameter estimation for such models is undertaken by maximum-likelihood techniques. In this paper maximum likelihood estimates are obtained for an empirical problem and compared with ordinary least-squares estimators. Results show substantial differences between least-squares and maximum-likelihood estimates, indicating a possibility for serious errors by using least-squares methods on models with a doubly limited dependent variable.     

MODELING STABILIZATION POLICIES IN A FINANCIALLY UNSTABLE ECONOMY

A non‐linear macrodynamic model is presented here to study possible stabilization policies in a financially unstable economy. Three policy rules will be considered, namely the interest rate rule (also called Taylor rule), the money supply rule and the fiscal policy rule. It will be shown that the interest rate rule can be used to stabilize a financially unstable economy on a ‘desired’ growth path. However, when the economy falls into a ‘liquidity trap’, the interest rate rule is ineffective, and therefore the fiscal policy rule should be employed. We also find a rule of money supply that can deal with the problem of government debt while the rest of the economy can still be stabilized on the ‘desired’ growth path.     

Those Current Account Imbalances: A Sceptical View1

The international current account imbalances, where the United States has a vast deficit, and several countries, notably Japan, China, Germany and the oil exporters have corresponding surpluses, are usually seen as problems. The argument here is that current account imbalances simply indicate intertemporal trade – the exchange of goods and services for claims. There are likely to be gains from trade of that kind as from ordinary trade. What, then, are the problems? This paper considers five scenarios, notably one where net savings of the surplus countries decline so that the world real interest rate rises, and another where the US fiscal deficit is reduced, so that the world real interest rate falls and there could be a worldwide aggregate demand problem, essentially caused by the high net savings of the surplus countries. The paper reviews the reasons for the large surpluses in terms of savings and investment ratios (especially China) and also discusses the long‐term problem for the United States. While four of the scenarios involve a decline in the dollar, they do not necessarily imply a sudden – and even ‘disruptive’– dollar crisis.     

A Note on the Nelson–Siegel Family

We study a problem posed in Bj"ork and Christensen (1999): Does there exist any nontrivial interest rate model that is consistent with the Nelson–Siegel family? They show that within the Heath–Jarrow–Morton framework with deterministic volatility structure the answer is no. In this paper we give a generalized version of this result including stochastic volatility structure. For that purpose we introduce the class of consistent state space processes, which have the property to provide an arbitrage-free interest rate model when representing the parameters of the Nelson–Siegel family. We characterize the consistent state space Itô processes in terms of their drift and diffusion coefficients. By solving an inverse problem we find their explicit form. It turns out that there exists no nontrivial interest rate model driven by a consistent state space Itô process.     

Self-Sabotage and Durable-Goods Monopoly

We analyze a simple two-period linear demand durable-goods monopoly model with “self-sabotage.” The firm has the ability to sabotage its own production by increasing its future (period two) manufacturing costs. We find that an uncommitted monopoly seller has an incentive to engage in such self-sabotage, while a committed seller or renter has no such incentive. Unlike the previous papers on self-sabotage, we show this occurs even though the firm faces no rivals in the output market. In our durable-goods setting, the incentive for self-sabotage arises from the seller’s commitment problem with period-one buyers (the so-called Coase conjecture). Interestingly, we also find that this sort of self-sabotage can not only be profit enhancing for the uncommitted firm, but may also increase social welfare (in contrast to the earlier models on self-sabotage.)