Multi-period mean–variance asset–liability management with uncontrolled cash flow and uncertain time-horizon

This paper considers an asset–liability management problem under a multi-period mean–variance model with uncontrolled cash flow and uncertain time-horizon. The difference from the existing literature is that the liability is assumed to be influenced not only by the stochastic return of the liability but also by some uncontrolled cash flows, which can be explained as, for example, stochastic expenditure of individual investors, or claim processes of insurers. Firstly, the original problem is translated into a standard multi-period stochastic optimal control problem by introducing a Lagrange multiplier, and the corresponding analytical solution is derived by adopting the dynamic programming approach. Secondly, according to Lagrange duality theorem, closed-form expressions for the efficient investment strategy and the mean–variance efficient frontier are obtained. Moreover, a multi-period version of two-fund separation theorem is proved, and some special cases are discussed. Finally, some numerical examples are presented to illustrate our results.     

Recursive utility and optimal capital accumulation II: sensitivity and duality theory

Summary This paper provides sensitivity and duality results for continuous-time optimal capital accumulation models where preferences belong to a class of recursive objectives. We combine the topology used by Becker, Boyd and Sung (1989) with a controllability condition to demonstrate that optimal paths are continuous with respect to changes in both the initial capital stock, and the rate of time preference. Under convexity and an interiority condition, we find the value function is differentiable, and derive a multiplier equation for the supporting prices. Finally, under some mild additional conditions, we show that supporting prices obeying the transversality and multiplier equations are both necessary and sufficient for an optimum.Robert Becker acknowledges the research support of National Science Foundation Grant SES 85-20180. We also thank Gerhard Sorger and the participants at the Northwestern Summer Workshop in Capital Theory and Monetary Economics for their helpful comments and suggestions.     

Is fiscal expansion more effective in a financial crisis?

After the Great Recession, the Keynesian expansionary policy has been regarded as an effective measure, especially under imperfect financial market conditions. Among literature related to fiscal policy in financial crises, Fernández-Villaverde (2010) suggests that the fiscal policy multiplier increases in a financial crisis through the Fisher effect. However, we should note that the author simply compared the multiplier computed in the standard new Keynesian dynamic stochastic general equilibrium (DSGE) with that in the DSGE with financial accelerator settings. As the financial accelerator is considered effective during both financial crises and normal financial conditions, the author’s comparison should be considered insignificant for showing a greater multiplier in the financial crisis. In this study, to make the exact comparison, we first estimate parameters regarding the Fisher effect under each regime separately and then compute and compare the estimated fiscal multipliers using these 2 estimates in the same DSGE model. Using Japanese financial data that provide enough observations under the good and bad regimes of financial conditions, we find that fiscal multipliers are smaller in the bad regime than in the good regime.     

Tests of restrictions in large demand systems

This paper compares some asymptotic tests of linear restrictions, using exact results and Monte Carlo methods, in systems which contain the same regressors in each equation. It is found that under a variety of conditions, a statistic suggested by Deaton provides a better approximation to the true distribution in small sample situations than the Wald, likelihood ratio or Lagrange multiplier tests.     

A comparison of classical tests of criterion when determining Granger causality with a bivariate ARMA model

The necessary and sufficient conditions for determining Granger causality with a bivariate ARMA model have been presented by Granger (1969), Haugh and Pierce (1977) and Eberts and Steece (1984). However the literature fails to address the question as to which classical test criterion likelihood ratio, Lagrange multiplier, Rao efficient scoring or Wald should be employed. This study addresses this question via a simulation study.The author would like to acknowledge numerous suggestions and insight provided by Bert Steece and Sergio Koreisha, along with two anonymous referees.     

金融资产收益率波动预测——基于我国股票市场跳跃行为研究

金融资产收益率波动是资产定价和金融风险管理的核心部分,而跳跃是收益率波动中的重要组成部分。基于修正Z-检验,本文检测识别我国股市波动中跳跃行为,并且研究了跳跃的时序特征,统计结果表明,在市场大波动时期,和连续成份相比,跳跃对于波动率具有极其重要的贡献。建立包含跳跃的已实现波动率非齐次自回归模型,在波动模型中纳入滞后绝对日收益率和杠杆效应预测股指收益率波动。实证分析结果显示,对于短期的波动预测,包含跳跃和两种影响因素的波动模型表现最好,然而对于提前1月的长期预测,跳跃和连续波动成份分离模型预测明显优于其它模型,这些事实说明跳跃对股指波动率预测具有重要的影响,好坏消息对波动率非对称性具有短期显著影响,而对长期水平的波动率预测影响不显著。     

A Lagrange multiplier stationarity test using covariates

A stationarity test based on the Lagrange multiplier using covariates is proposed. The tests are shown to have more power than standard Lagrange multiplier tests if the covariates are highly correlated with the stationary part of the data.     

Foreign equity option pricing under stochastic volatility model with double jumps

This paper considers the challenging problem advocated by Huang and Hung (2005), that is to incorporate the stochastic volatility into the foreign equity option pricing. Foreign equity options (quanto options) are contingent claims where the payoff is determined by an equity in one currency but the actual payoff is done in another currency. Huang and Hung (2005) priced foreign equity options under the Lévy processes. In Huang and Hung's paper, they considered jumps in the foreign asset prices and exchange rates and assumed the volatility as constant. However, many studies showed that constant volatility and jumps in returns are incapable of fully capturing the empirical features of equity returns or option prices. In this paper, the stochastic volatility with simultaneous jumps in prices and volatility is proposed to model foreign asset prices and exchange rates. The foreign equity option pricing formula is given by using the Fourier inverse transformation. The numerical results show that the use of stochastic volatility with simultaneous jumps in prices and volatility proposed to model foreign asset prices and exchange rates is necessary and this approach can help us to capture more accurately the foreign equity option prices.     

A new test for chaos and determinism based on symbolic dynamics

We propose a novel test to determine, given a time series, if the dynamics are generated by a deterministic (including low dimensional chaos), rather than a stochastic, process. In addition, we introduce a new nonparametric bootstrap test for independence which is consistent against a broad class of alternatives. The conditions under which the tests can be applied are very weak. The advantages of the presented methods are simplicity, invariance with respect to monotonic transformations and the applicability of the tests regardless of the discrete or continuous nature of the data generating process. We conduct several simulation studies to evaluate the performance of our tests on well-known dynamic processes. Finally, our tests are applied to several sets of financial returns that have been recently studied.     

On the Stochastic Properties of Carbon Futures Prices

Pricing carbon is a central concern in environmental economics, due to the worldwide importance of emissions trading schemes to regulate pollution. This paper documents the presence of small and large jumps in the stochastic process of the CO $_2$ futures price. The large jumps have a discrete origin, i.e. they can arise from various demand factors or institutional decisions on the tradable permits market. Contrary to the existing literature, we show that the stochastic process of carbon futures prices does not contain a continuous component (Brownian motion). The results are derived by using high-frequency data in the activity signature function framework (Todorov and Tauchen in J Econom 154:125–138, 2010; Todorov and Tauchen in J Bus Econ Stat 29:356–371, 2011). The implication is that the carbon futures price should be modeled as an appropriately sampled, centered Lévy or Poisson process. The pure-jump behavior of the carbon price might be explained by the lower volume of trades on this allowance market (compared to other highly liquid financial markets).     

Optimality for controlled jump processes: a simple approach

Summary This note presents a very simple method for deriving the necessary optimality conditions for optimal control of jump (point) processes. By means of Bellman's principle of optimality, the original stochastic control problem is transformed into a simple optimization problem. The derivation is remarkably simpler than the existing ones in the literature.I am grateful to the referee for many useful comments and suggestions. This research was supported in part by the Bradley Foundation and the Hewlett Foundation.     

Asset allocation under stochastic interest rate with regime switching

We investigate an optimal asset allocation problem in a Markovian regime-switching financial market with stochastic interest rate. The market has three investment opportunities, namely, a bank account, a share and a zero-coupon bond, where stochastic movements of the short rate and the share price are governed by a Markovian regime-switching Vasicek model and a Markovian regime-switching Geometric Brownian motion, respectively. We discuss the optimal asset allocation problem using the dynamic programming approach for stochastic optimal control and derive a regime-switching Hamilton–Jacobi–Bellman (HJB) equation. Particular attention is paid to the exponential utility case. Numerical and sensitivity analysis are provided for this case. The numerical results reveal that regime-switches described by a two-state Markov chain have significant impacts on the optimal investment strategies in the share and the bond. Furthermore, the market prices of risk in both the bond and share markets are crucial factors in determining the optimal investment strategies.     

Financial liberalization and the stationarity of money multiplier

Abstract

In countries without an explicit inflation targeting mechanism, a stable relationship between the monetary base and the money supply allows policymakers to implement changes in monetary policy with a reasonable degree of certainty about the impact on the money supply. The relationship can, however, be influenced by major structural shifts such as financial sector reforms. The present study finds that when structural change bought about by financial liberalisation is ignored, the unit root hypothesis is spuriously accepted. However, once this break is incorporated into the analysis, the multiplier exhibits no presence of a stochastic trend.     

Optimal Management of Environmental Externalities with Time Lags and Uncertainty

Many environmental externalities occur with time lags that can range from a few days to several centuries in length, and many of these externalities are also subject to uncertainty. In this paper, we examine the key features of an optimal policy to manage environmental externalities that are both lagged and stochastic. We develop a two-period, two-polluter model and obtain closed-form solutions for optimal emissions levels under different combinations of damage functions and stochastic processes. These solutions show that it is not obvious whether greater control should be exerted on polluters that generate externalities with longer lags or on polluters that generate externalities with shorter lags. We find that the optimal ranking of polluters with respect to the length of the time lag associated with their externality will depend on (a) the discount rate, (b) conditional expectations of future states of the polluted resource, (c) persistence of the pollutant, and (d) initial conditions.     

Stochastic convexity in dynamic programming

Summary. This paper explores sufficient conditions for a continuous stationary Markov optimal policy and a concave value function in stochastic dynamic programming problems. Also, the paper addresses conditions needed for the differentiability of the value function. The paper uses conditions such as first order stochastic dominance, second order stochastic dominance and concave stochastic dominance that are widely applied in economics. Received: February 23, 2001; revised version: May 19, 2002 RID="*" ID="*" I am deeply indebted to Prajit Dutta for patient assistance and advice. This paper has benefited from discussions with Tsz Cheong Lai, Tackseung Jun, Werner Stanzl and Satyajit Bose as well as feedback from an anonymous referee.     

Are rich people smarter?

We formulate a general stochastic process of wealth accumulation by capital investment and analyze the conditions required to ensure convergence to the empirically observed Pareto wealth distribution. While homogeneous investment talent leads to the Pareto distribution under very general conditions, even a mild degree of differential investment talent results in a non-Pareto wealth distribution. This finding suggests that chance, rather than differential investment talent, is the dominant factor in the process of wealth accumulation by financial investment. Our findings conform with market efficiency and may have implications regarding the origins, the economic significance, and the social desirability of wealth inequality at the high-wealth range.     

Computation of non-linear continuous optimal growth models: experiments with optimal control algorithms and computer programs

In this paper we discuss the use of optimal control methods for computing non-linear continuous optimal growth models. We have discussed various recently developed algorithms for computing optimal control, involving step-function approximations, Runge–Kutta solutions of differential equations, and we suggest that the discretization approach is preferable to methods which solve first-order optimality conditions. We have surveyed some powerful computer programs by : , and for computing such models numerically. These programs have no substantial optimal growth modelling applications yet, although they have numerous engineering and scientific applications. A computer program named by is developed in this study. Results are reported for computing the Kendrick–Taylor optimal growth model using and programs based on the discretization approach. References are made to the computational experiments with and . The results are used to compare and evaluate mathematical and economic properties, and computing criteria. While several computer packages are available for optimal control problems, they are not always suitable for particular classes of control problems, including some economic growth models. The -based and , however, offer good opportunities for computing continuous optimal growth models. It is argued in this paper, that optimal growth modellers may find that these recently developed algorithms and computer programs are relatively preferable for a large variety of optimal growth modelling studies.     

Stability with regime switching

The purpose of this paper is to analyze the stability of systems of piecewise continuous differential equations, and to apply the results to a disequilibrium economic model. The discontinuity problem appears in disequilibrium models because of the so-called “short-side” rule. The concept of Filippov solution makes it possible to analyze the dynamic evolution of such a model. This paper demonstrates that (i) stability conditions for each subsystem are neither necessary nor sufficient for overall stability, except in special cases such as a system of linear differential equations in R² with two regimes separated by a linear boundary; (ii) several sufficient conditions for overall stability with many regimes are available; and (iii) stability theorems with regime switching are useful for disequilibrium economic models with several regimes.     

Mutual fund separation in financial theory—The separating distributions

This paper finds necessary and sufficient conditions on the stochastic structure of asset returns for portfolio choice to be equivalent to choice among a limited number of mutual funds of assets, independent of investors' preferences. This type of separation result is central to modern financial theory and the distributions which satisfy these conditions, the separating distributions, form the underlying basis for much of this theory.     

A simple and efficient test for the Pareto law

This note presents a simple and locally optimal test statistic for the Pareto law. The test is based on the Lagrange multiplier principle and can be computed easily once the maximum likelihood estimator of the scale parameter of the Pareto density has been obtained. A Monte Carlo exercise shows the good small sample properties of the test under the null of the Pareto law and also its power against some sensible and interesting alternatives. In addition, the proposed test is compared to a goodness of fit test which is powerful against more or less all alternatives. Eventually, a simple application to urban economics is performed.