Asymptotically optimal dividend policy for regime-switching compound Poisson models

This work develops asymptotically optimal dividend policies to maximize the expected present value of dividends until ruin.Compound Poisson processes with regime switching are used to model the surplus and the switching（a continuous-time controlled Markov chain） represents random environment and other economic conditions.Assuming the switching to be fast varying together with suitable conditions,it is shown that the system has a limit that is an average with respect to the invariant measure of a related Markov chain.Under simple conditions,the optimal policy of the limit dividend strategy is a threshold policy.Using the optimal policy of the limit system as a guide,feedback control for the original surplus is then developed.It is demonstrated that the constructed dividend policy is asymptotically optimal.     

Comparative Study on Heat Transfer Enhancement of Low Volume Concentration of Al2o3–Water and Carbon Nano-Tube–Water Nano-Fluids in Transition Regime Using Helical Screw Tape Inserts

This study reports the comparison of heat transfer and friction factor characteristics of helical screw inserts in Al₂O₃–water and carbon nano-tube–water nano-fluids through a straight pipe in transition regime with constant heat flux boundary condition. Experiments were carried out by using 0.15% volume concentration of Al₂O₃–water and carbon nano-tube–water nano-fluid with helical tape inserts of twist ratio, TR = 1.5, 2.5, and 3. The thermal performance of helical screw tape inserts with the carbon nano-tube–water nano-fluid is found -to be higher when compared to the Al₂O₃–water nano-fluid. In addition, the maximum enhancement in heat transfer was obtained for the carbon nano-tube–water nano-fluid with helical tape inserts of twist ratio 1.5. The increase in pressure drop of the Al₂O₃–water nano-fluid with helical screw tape inserts is found to be higher compared to the carbon nano-tube–water nano-fluid helical screw tape inserts at lower value of twist ratio.     

Stochastic impulse control with regime switching for the optimal dividend policy when there are business cycles,taxes and fixed costs

We consider the problem of finding the optimal dividend policy for a company whose cash reserve follows a Brownian motion with drift and volatility modulated by an observable finite-state continuous-time Markov chain. The Markov chain represents the regime of the economy. We allow fixed costs and taxes associated with the dividend payments. This optimization problem generates a stochastic impulse control problem with regime switching. We solve this problem and obtain the first analytical solutions for the optimal dividend policy when there are simultaneously fixed costs, taxes and business cycles. Our results show that the optimal dividend policy depends strongly on the regime of the economy, on fixed costs and on taxes.     

American Options in the Heston Model with Stochastic Interest Rate and Its Generalizations

Abstract

We consider the Heston model with the stochastic interest rate of Cox–Ingersoll–Ross (CIR) type and more general models with stochastic volatility and interest rates depending on two CIR-factors; the price, volatility and interest rate may correlate. Time-derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options arising in the time discretization of a Markov-modulated Lévy model. Options in this sequence are solved using an iteration method based on the Wiener–Hopf factorization. Typical shapes of the early exercise boundary are shown, and good agreement of option prices with prices calculated with the Longstaff–Schwartz method and Medvedev–Scaillet asymptotic method is demonstrated.     

Option pricing when asset returns jump interruptedly

This paper proposes an extension of Merton's jump‐diffusion model to reflect the time inhomogeneity caused by changes of market states. The benefit is that it simultaneously captures two salient features in asset returns: heavy tailness and volatility clustering. On the basis of an empirical analysis where jumps are found to happen much more frequently in risky periods than in normal periods, we assume that the Poisson process for driving jumps is governed by a two‐state on‐off Markov chain. This makes jumps happen interruptedly and helps to generate different dynamics under these two states. We provide a full analysis for the proposed model and derive the recursive formulas for the conditional state probabilities of the underlying Markov chain. These analytical results lead to an algorithm that can be implemented to determine the prices of European options under normal and risky states. Numerical examples are given to demonstrate how time inhomogeneity influences return distributions, option prices, and volatility smiles. The contrasting patterns seen in different states indicate the insufficiency of using time‐homogeneous models and justify the use of the proposed model. Copyright © 2012 John Wiley & Sons, Ltd.     

资本账户开放对浮动汇率制度福利的非线性效应:以新兴市场经济体为例

通过构建一个带有随机冲击的开放经济模型,采用比较静态分析与动态分析相结合的方法,探讨了新兴市场经济体资本账户开放对浮动汇率制度福利变化的影响.结果显示,资本账户开放度对浮动汇率制度的福利变化具有显著的非线性效应.浮动汇率制度"吸收器"功能的有效发挥不仅取决于一国资本账户开放度偏离其最优资本账户开放度的位置,还受本国资本账户开放度变化量的影响.得到我国资本账户开放进程中人民币汇率制度改革的启示是:我国仍应在坚持可控、渐进的原则下,逐步推进人民币汇率制度改革与资本账户开放,并注意两者之间的搭配与协调.     

Model flames in the Boussinesq limit: Rising bubbles

Using the Boussinesq buoyancy approximation, we study a bubble of reaction products rising in the reactant fluid under the influence of gravity. Reaction on the surface of the bubble (the flame) results in an increase of the volume of the bubble. We consider fluids with low Prandtl and high Froude numbers (heat diffusion dominates over viscous dissipation, and burning dominates over gravitational effects). We show that, under these conditions, all initially small bubbles follow the same growth pattern, regardless of the flame speed, the reaction type, the gravity, the viscosity, the initial size, and, to some extent, the initial shape of the bubble. In the initial stage of this similarity solution a bubble grows radially in an essentially motionless fluid until it reaches some critical size, which is determined by the laminar flame speed, the gravitational acceleration, and the Atwood number. Once the bubble reaches the critical size, convection becomes significant and the bubble evolves into a more complicated, mushroom-like shape. The similarity solution is expressed using the critical bubble size for the unit length and the critical size divided by the laminar flame speed as the unit time.     

Towards a classification of models for the numerical simulation of premixed combustion based on a generalized regime diagram

The inner structure, and the physical behaviour of turbulent premixed flames are usually described, and classified by means of the regime diagram introduced by Borghi and Peters. Thereby properties related to both the flame and the (turbulent) flow are considered. In this work a diagram valid for all physical regimes, comprising suitable requirements for laminar simulations, direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds averaging based numerical simulation (RANS) is proposed. In particular the diagram describes essential situations within the validity limits of the “Borghi, Peters diagram” which physical phenomena are resolved by the simulation, and which have to be modelled. This information is used for systematic classification of various models by suggesting specific models that are appropriate depending on the regime and numerical resolution, and may provide guidance for numerical simulation methods and model development in turbulent premixed combustion. This might help users as a guideline in choosing appropriate models for a given device, and numerical effort available. The regime diagram suggested by Pitsch and Duchamp de Lageneste, which includes DNS and LES by explicitely accounting for the numerical related variable filterwidth, emerges here as one of the special two-dimensional cases possible. In contrast to the generalized regime diagram, their diagram does not include laminar simulations, and RANS based considerations, while transition between wrinkled and corrugated flamelets is not clearly established.     

Exploration of fractal nature of WO3 nanowire aggregates

The morphology of WO₃ aggregates formed by irregular nanoparticles (D∼40 nm) and nanowires of different aspect ratios (2, 4, 6, and 10 μm nominal lengths) dispersed in commonly used polar solvents without dispersant agents is investigated using a small-angle light scattering technique and by means of fractal theory. Nanoparticles form compact spherical aggregates (D_f∼2.6), whereas 2 μm nanowires with low aspect ratio (L/D∼10) follow a slow cluster-cluster aggregation mechanism with no discernable change in fractal dimension (D_f=2.1) monitored in an extended period of 6 months, despite a notable growth in size (R_g=2.3-3.1 μm). For higher aspect ratio nanowires, scattered intensity profiles, which migrate towards the Porod regime, qualitatively obey the Lorenz-Mie theory predictions. The 10 μm nanowires with very high aspect ratio (L/D∼250) are observed to form stable dispersions in a time span of 6 days. Analytical methods based on spherical primary particle formulations predict D_f=1.9, 1.7, and 1.4 for 4, 6, and 10 μm nanowires, respectively.