OPTIMAL REINSURANCE AND DIVIDEND DISTRIBUTION POLICIES IN THE CRAMÉR-LUNDBERG MODEL

We consider that the reserve of an insurance company follows a Cramér-Lundberg process. The management has the possibility of controlling the risk by means of reinsurance. Our aim is to find a dynamic choice of both the reinsurance policy and the dividend distribution strategy that maximizes the cumulative expected discounted dividend payouts. We study the usual cases of excess-of-loss and proportional reinsurance as well as the family of all possible reinsurance contracts. We characterize the optimal value function as the smallest viscosity solution of the associated Hamilton-Jacobi-Bellman equation and we prove that there exists an optimal band strategy. We also describe the optimal value function for small initial reserves.     

OPTIMAL EXECUTION OF A VWAP ORDER: A STOCHASTIC CONTROL APPROACH

We consider the optimal liquidation of a position of stock (long or short) where trading has a temporary market impact on the price. The aim is to minimize both the mean and variance of the order slippage with respect to a benchmark given by the market volume‐weighted average price (VWAP). In this setting, we introduce a new model for the relative volume curve which allows simultaneously for accurate data fit, economic justification, and mathematical tractability. Tackling the resulting optimization problem using a stochastic control approach, we derive and solve the corresponding Hamilton–Jacobi–Bellman equation to give an explicit characterization of the optimal trading rate and liquidation trajectory.     

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.     

A NONLINEAR BUSINESS CYCLE MODEL IN DISCRETE TIME

The paper develops a simple multiplier-accelerator model of a market economy, where the strength of the accelerator relationship between current investment and past output depends on the state of the economy. It is found that the greater the values of the multiplier and the accelerator, the more persistent and aperiodic («chaotic») would be the cyclical behaviour of the economy.     

有源电力滤波器的小波变换-灰色预测控制

利用单子带重构改进小波变换算法克服了传统小波变换算法存在频率混叠现象的固有缺陷,取得了精确的指令电流值。在负荷电流灰色预测和APF超前指令电流生成方面,确定了适合APF实验系统的灰色预测参数。负荷突变条件下的仿真分析表明,小波变换-灰色预测控制APF控制方面可有效、快速地检测出APF中的谐波电流,并有效地补偿了系统自身固有延时。为电力系统谐波检测和抑制提供了一种新的思路。     

OPTIMAL CONSUMPTION AND INVESTMENT FOR A LARGE INVESTOR: AN INTENSITY‐BASED CONTROL FRAMEWORK

We introduce a new stochastic control framework where in addition to controlling the local coefficients of a jump‐diffusion process, it is also possible to control the intensity of switching from one state of the environment to the other. Building upon this framework, we develop a large investor model for optimal consumption and investment that generalizes the regime‐switching approach of Bäuerle and Rieder (2004) .     

A STATE‐CONSTRAINED DIFFERENTIAL GAME ARISING IN OPTIMAL PORTFOLIO LIQUIDATION

We consider n risk‐averse agents who compete for liquidity in an Almgren–Chriss market impact model. Mathematically, this situation can be described by a Nash equilibrium for a certain linear quadratic differential game with state constraints. The state constraints enter the problem as terminal boundary conditions for finite and infinite time horizons. We prove existence and uniqueness of Nash equilibria and give closed‐form solutions in some special cases. We also analyze qualitative properties of the equilibrium strategies and provide corresponding financial interpretations.     

ON OPTIMAL INVESTMENT FOR A BEHAVIORAL INVESTOR IN MULTIPERIOD INCOMPLETE MARKET MODELS

We study the optimal investment problem for a behavioral investor in an incomplete discrete‐time multiperiod financial market model. For the first time in the literature, we provide easily verifiable and interpretable conditions for well‐posedness. Under two different sets of assumptions, we also establish the existence of optimal strategies.     

OPTIMAL LIQUIDATION IN A LIMIT ORDER BOOK FOR A RISK‐AVERSE INVESTOR

In a limit order book model with exponential resilience, general shape function, and an unaffected stock price following the Bachelier model, we consider the problem of optimal liquidation for an investor with constant absolute risk aversion. We show that the problem can be reduced to a two‐dimensional deterministic problem which involves no buy orders. We derive an explicit expression for the value function and the optimal liquidation strategy. The analysis is complicated by the fact that the intervention boundary, which determines the optimal liquidation strategy, is discontinuous if there are levels in the limit order book with relatively little market depth. Despite this complication, the equation for the intervention boundary is fairly simple. We show that the optimal liquidation strategy possesses the natural properties one would expect, and provide an explicit example for the case where the limit order book has a constant shape function.     

OPTIMAL INTERNATIONAL DEBT AND ENDOGENOUS TIME PREFERENCE IN A DEMOGRAPHICALLY DIVIDED WORLD (*)

The international transmission of shocks in population growth and technology is examined in an interdependent two-country world economy; decisions concerning the intertemporal allocation are made by social planners with an infinite horizon and an endogenous rate of time preference. Steady state shocks in population growth are shown to be negatively transmitted to the rate of time preference. In the steady state, the optimal foreign debt is determinate and it brings about a convergence of time preference. The net creditor and debtor positions in the steady state depend on the discount rate functions, the states of technology and the rates of population growth.     

COMPARATIVE DYNAMICS AND OPTIMAL FISCAL POLICY IN A SIMPLE MODEL OF ENDOGENOUS GROWTH

I analyze optimal fiscal policy choices in a continuous time endogenous growth model similar to Barro’s. The government uses income taxes from representative ‘rich’ and ‘poor’ households to finance purchases of productive goods and to make transfer payments to poor households. Increases in government purchases can increase the growth rate, while increases in transfers reduce growth. I examine the socially optimal allocation of government resources to purchases and transfer payments and describe conditions under which both the rich and poor would benefit from cuts in entitlements if the savings are used to finance increased government purchases of productive goods.     

NOTE ON THE WELFARE EFFECT OF SECOND‐BEST POLICIES IN A NETWORK INDUSTRY: A MONOPOLY CASE

We show that the welfare effect of second‐best policies such as a subsidy/tax and quality regulation in the case of a monopoly in a network industry depends on the strength of network effects. That is, focusing on the case in which the network effect is smaller (larger) than the marginal cost of production for the small (large) network effect, it is demonstrated that in the case of a small (large) network effect, an output and a quality‐improving subsidy (tax) policy are socially optimal, and a government should commit to a minimum (maximum) quality standard.     

OPTIMAL HIGH‐FREQUENCY TRADING IN A PRO RATA MICROSTRUCTURE WITH PREDICTIVE INFORMATION

We propose a framework to study optimal trading policies in a one‐tick pro rata limit order book, as typically arises in short‐term interest rate futures contracts. The high‐frequency trader chooses to post either market orders or limit orders, which are represented, respectively, by impulse controls and regular controls. We discuss the consequences of the two main features of this microstructure: first, the limit orders are only partially executed, and therefore she has no control on the executed quantity. Second, the high‐frequency trader faces the overtrading risk, which is the risk of large variations in her inventory. The consequences of this risk are investigated in the context of optimal liquidation. The optimal trading problem is studied by stochastic control and dynamic programming methods, and we provide the associated numerical resolution procedure and prove its convergence. We propose dimension reduction techniques in several cases of practical interest. We also detail a high‐frequency trading strategy in the case where a (predictive) directional information on the price is available. Each of the resulting strategies is illustrated by numerical tests.     

A CONVENIENT MULTISECTORAL POLICY CONTROL FOR ICT IN THE US ECONOMY

Through the application of the Macro Multiplier (MM) approach on an Input–Output matrix for US economy in year 2005, the paper identifies the ‘convenient’ structure of a policy control on final demand, oriented to a particular policy objective. The approach quantifies a set of aggregated scale effects, called MM, and the associated structures of both policy and objective variables. In this way the policy maker can both get a complete picture of the patterns of the objective that can be attained and determine a ‘convenient’ structure of the policy variable that compels the model towards those patterns.     

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.