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.     

Should Stochastic Volatility Matter to the Cost-Constrained Investor?

Significant strides have been made in the development of continuous-time portfolio optimization models since Merton (1969) . Two independent advances have been the incorporation of transaction costs and time-varying volatility into the investor's optimization problem. Transaction costs generally inhibit investors from trading too often. Time-varying volatility, on the other hand, encourages trading activity, as it can result in an evolving optimal allocation of resources. We examine the two-asset portfolio optimization problem when both elements are present. We show that a transaction cost framework can be extended to include a stochastic volatility process. We then specify a transaction cost model with stochastic volatility and show that when the risk premium is linear in variance, the optimal strategy for the investor is independent of the level of volatility in the risky asset. We call this the Variance Invariance Principle.     

Dynamic Optimization of Long-Term Growth Rate for a Portfolio with Transaction Costs and Logarithmic Utility

We study the optimal investment policy for an investor who has available one bank account and n risky assets modeled by log-normal diffusions. The objective is to maximize the long-run average growth of wealth for a logarithmic utility function in the presence of proportional transaction costs. This problem is formulated as an ergodic singular stochastic control problem and interpreted as the limit of a discounted control problem for vanishing discount factor. The variational inequalities for the discounted control problem and the limiting ergodic problem are established in the viscosity sense. The ergodic variational inequality is solved by using a numerical algorithm based on policy iterations and multigrid methods. A numerical example is displayed for two risky assets.     

Optimal Investment and Consumption With Two Bonds and Transaction Costs1

An agent can invest in a high-yield bond and a low-yield bond, holding either long or short positions in either asset. Any movement of money between these two assets incurs a transaction cost proportional to the size of the transaction. the low-yield bond is liquid in the sense that wealth invested in this bond can be consumed directly without a transaction cost; wealth invested in the high-yield bond can be consumed only by first moving it into the low-yield bond. the problem of optimal consumption and investment on an infinite planning horizon is solved for a class of utility functions larger than the class of power functions.     

HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH12

We derive a formula for the minimal initial wealth needed to hedge an arbitrary contingent claim in a continuous-time model with proportional transaction costs; the expression obtained can be interpreted as the supremum of expected discounted values of the claim, over all (pairs of) probability measures under which the “wealth process” is a supermartingale. Next, we prove the existence of an optimal solution to the portfolio optimization problem of maximizing utility from terminal wealth in the same model, we also characterize this solution via a transformation to a hedging problem: the optimal portfolio is the one that hedges the inverse of marginal utility evaluated at the shadow state-price density solving the corresponding dual problem, if such exists. We can then use the optimal shadow state-price density for pricing contingent claims in this market. the mathematical tools are those of continuous-time martingales, convex analysis, functional analysis, and duality theory.     

A NOTE ON THE EFFECTS OF TAXES ON OPTIMAL INVESTMENT

We integrate two approaches to portfolio management problems: that of Morton and Pliska (1995) for a portfolio with risky and riskless assets under transaction costs, and that of Cadenillas and Pliska (1999) for a portfolio with a risky asset under taxes and transaction costs. In particular, we show that the two surprising results of the latter paper, results shown for a taxable market consisting of only a single security, extend to a financial market with one risky asset and one bond: it can be optimal to realize not only losses but also gains, and sometimes the investor prefers a positive tax rate.     

我国电子商务企业自建物流现状及对策——基于企业边界视角

物流对电子商务的发展有着十分重要的影响,随着我国电子商务企业规模的急剧扩大,自建物流成为一种趋势。电子商务企业自建物流受交易成本、核心能力的制约,存在着过度依赖外部投资、区域发展不平衡、竞争激烈导致的利润率低、外部环境差、管理成本高等方面的问题,应从打造品牌、转变发展方式、电子商务企业与快递企业建立战略合作伙伴关系等方面寻求出路。     

论供应链成本控制

供应链成本控制对象主要是交易成本和作业成本,在网络信息技术的环境下,降低交易成本应采用ERP等系统,以此加强信息的交互或共享,从而达到降低交易成本的目的。对于各链节成员企业的作业成本的控制,应引入作业管理的思想,在各节点企业构建作业中心,以作业中心作为成本控制的责任中心,分别采取作业消除、作业改善和作业再造等方法和手段,从而达到降低整个供应链作业成本、提高供应链效率的目的。     

PORTFOLIO OPTIMIZATION WITH JUMPS AND UNOBSERVABLE INTENSITY PROCESS

We consider a financial market with one bond and one stock. The dynamics of the stock price process allow jumps which occur according to a Markov-modulated Poisson process. We assume that there is an investor who is only able to observe the stock price process and not the driving Markov chain. The investor's aim is to maximize the expected utility of terminal wealth. Using a classical result from filter theory it is possible to reduce this problem with partial observation to one with complete observation. With the help of a generalized Hamilton–Jacobi–Bellman equation where we replace the derivative by Clarke's generalized gradient, we identify an optimal portfolio strategy. Finally, we discuss some special cases of this model and prove several properties of the optimal portfolio strategy. In particular, we derive bounds and discuss the influence of uncertainty on the optimal portfolio strategy.