摩擦市场的最优消费-投资组合选择

本文研究摩擦市场中的最优消费-投资组合选择问题.当金融资产和自然状态个数为有限个以及摩擦局限于成比例的交易费时,可用原始市场或适当转换了的市场的无套利性来刻画最优消费-投资组合策略的存在性或充要条件.     

摩擦市场的利率期限结构的无套利分析

本文用无套利方法分析有摩擦金融市场中利率的期限结构.对存在有限个债券和离散有限个到期日以及存在成比例的交易费、买卖差价、税赋这三种摩擦的金融市场,引入了相容期限结构的概念,给出了相容期限结构和套利机会的存在性结果或充要条件及它们的识别与计算方法.     

Equivalent martingale measures for large financial markets in discrete time

We show that in a discrete-time large financial market the absence of certain asymptotic arbitrage opportunities is equivalent to the existence of martingale measures in a strong sense. We also consider the Arbitrage Pricing Model with stable random variables where we are able to give explicit necessary and sufficient conditions using market parameters.     

有交易成本的利率期限结构的分析

本文利用无套利均衡方法对存在着交易费，赋税，以及买卖差价等交易成本的债券市场进行分析．用数学方法严格地证明了一个基本结论：在有交易成本的债券市场上，弱无套利性与相容期限结构的存在性是等价的．     

Arbitrage theory for non convex financial market models

We propose a unified approach where a security market is described by a liquidation value process. This allows to extend the frictionless models of the classical theory as well as the recent proportional transaction costs models to a larger class of financial markets with transaction costs including non proportional trading costs. The usual tools from convex analysis however become inadequate to characterize the absence of arbitrage opportunities in non-convex financial market models. The natural question is to which extent the results of the classical arbitrage theory are still valid. Our contribution is a first attempt to characterize the absence of arbitrage opportunities in non convex financial market models.     

General financial market model defined by a liquidation value process

Financial market models defined by a liquidation value process generalize the conic models of Schachermayer and Kabanov where the transaction costs are proportional to the exchanged volumes of traded assets. The solvency set of all portfolio positions that can be liquidated without any debt is not necessary convex, e.g. in presence of proportional transaction costs and fixed costs. Therefore, the classical duality principle based on the Hahn–Banach separation theorem is not appropriate to characterize the prices super hedging a contingent claim. Using an alternative method based on the concepts of essential supremum and maximum, we provide a characterization of European and American contingent claim prices under the absence of arbitrage opportunity of the second kind.     

Strong asymptotic arbitrage in the large fractional binary market

We study, from the perspective of large financial markets, the asymptotic arbitrage (AA) opportunities in a sequence of binary markets approximating the fractional Black–Scholes model. This approximating sequence was introduced by Sottinen and named fractional binary market. The large financial market under consideration does not satisfy the standard assumptions of the theory of AA. For this reason, we follow a constructive approach to show first that a strong AA (SAA) exists in the frictionless case. Indeed, with the help of an appropriate version of the law of large numbers and a stopping time procedure, we construct a sequence of self-financing trading strategies leading to the desired result. Next, we introduce, in each small market, proportional transaction costs, and we show that a slight modification of the previous trading strategies leads to a SAA when the transaction costs converge fast enough to 0.     

Existence of a Radner equilibrium in a model with transaction costs

We prove the existence of a Radner equilibrium in a model with proportional transaction costs on an infinite time horizon and analyze the effect of transaction costs on the endogenously determined interest rate. Two agents receive exogenous, unspanned income and choose between consumption and investing into an annuity. After establishing the existence of a discrete-time equilibrium, we show that the discrete-time equilibrium converges to a continuous-time equilibrium model. The continuous-time equilibrium provides an explicit formula for the equilibrium interest rate in terms of the transaction cost parameter. We analyze the impact of transaction costs on the equilibrium interest rate and welfare levels.     

Optimal securitization of credit portfolios via impulse control

We study the optimal loan securitization policy of a commercial bank which is mainly engaged in lending activities. For this we propose a stylized dynamic model which contains the main features affecting the securitization decision. In line with reality we assume that there are non-negligible fixed and variable transaction costs associated with each securitization. The fixed transaction costs lead to a formulation of the optimization problem in an impulse control framework. We prove viscosity solution existence and uniqueness for the quasi-variational inequality associated with this impulse control problem. Iterated optimal stopping is used to find a numerical solution of this PDE, and numerical examples are discussed.     

Asymptotic analysis for Merton's problem with transaction costs in power utility case

We revisit the optimal investment and consumption problem with proportional transaction costs. We prove that both the value function and the slopes of the lines demarcating the no-trading region are analytic functions of cube root of the transaction cost parameter. Also, we can explicitly calculate the coefficients of the fractional power series expansions of the value function and the no-trading region.     

Growth Optimal Portfolio Selection Under Proportional Transaction Costs with Obligatory Diversification

A continuous time long run growth optimal or optimal logarithmic utility portfolio with proportional transaction costs consisting of a fixed proportional cost and a cost proportional to the volume of transaction is considered. The asset prices are modeled as exponent of diffusion with jumps whose parameters depend on a finite state Markov process of economic factors. An obligatory portfolio diversification is introduced, accordingly to which it is required to invest at least a fixed small portion of our wealth in each asset.     

Two-stage integer programs with stochastic right-hand sides: a superadditive dual approach

We consider two-stage pure integer programs with discretely distributed stochastic right-hand sides. We present an equivalent superadditive dual formulation that uses the value functions in both stages. We give two algorithms for finding the value functions. To solve the reformulation after obtaining the value functions, we develop a global branch-and-bound approach and a level-set approach to find an optimal tender. We show that our method can solve randomly generated instances whose extensive forms are several orders of magnitude larger than the extensive forms of those instances found in the literature. This work is supported by National Science Foundation grants DMI-0217190 and DMI-0355433.     

Asymptotic arbitrage in large financial markets with friction

In the modern version of arbitrage pricing theory suggested by Kabanov and Kramkov the fundamental financially meaningful concept is an asymptotic arbitrage. The ??real world?? large market is represented by a sequence of ??models?? and, though each of them is arbitrage free, investors may obtain non-risky profits in the limit. Mathematically, absence of the asymptotic arbitrage is expressed as contiguity of envelopes of the sets of equivalent martingale measures and objective probabilities. The classical theory deals with frictionless markets. In the present paper we extend it to markets with transaction costs. Assuming that each model admits consistent price systems, we relate them with families of probability measures and consider their upper and lower envelopes. The main result concerns the necessary and sufficient conditions for absence of asymptotic arbitrage opportunities of the first and second kinds expressed in terms of contiguity. We provide also more specific conditions involving Hellinger processes and give applications to particular models of large financial markets.     

Impulsive Control of Portfolios

In this paper a general model of a market with asset prices and economical factors of Markovian structure is considered. The problem is to find optimal portfolio strategies maximizing a discounted infinite horizon reward functional consisting of an integral term measuring the quality of the portfolio at each moment and a discrete term measuring the reward from consumption. There are general transaction costs which, in particular, cover fixed plus proportional costs. It is shown, under general conditions, that there exists an optimal impulse strategy and the value function is a solution to the Bellman equation which corresponds to suitable quasi-variational inequalities.     

Product damage and free sampling: a newsvendor model with passive and proactive self-consumption

A retailer sells a single product for a single period. During transportation and storage, some of these products are consumed by the retailer either (1) due to unavoidable damages (passive self-consumption), or (2) distributed for free to the customers (proactive self-consumption). This creates a mismatch between the amount purchased by the retailer and the amount available for sale. We study passive self-consumption with (i) fixed and (ii) proportional consumption, and proactive self-consumption with (iii) additive and (iv) multiplicative demand. Under proactive self-consumption, the retailer holds more inventory and receives a higher profit; the reverse is true under passive self-consumption. Yet, (i), (iii) and (iv) result in a higher order quantity and same fill rate compared to no self-consumption, (ii) may result in a higher or lower order quantity with a lower fill rate. When both types of self-consumption coexist, the optimal policy can be complicated. We characterize the optimal policy and show through numerical studies that the optimal policy can take at most three formats: sell to the market with positive proactive self-consumption, sell to the market with zero proactive self-consumption and do not sell to the market. Interestingly, the optimal order quantity is not smooth in the fraction of the proportional self-consumption. Further we find that when the market adoption rate is uncertain, the optimal strategy preserves a similar structure. The retailer benefits from expediting if the difference between the high and the low market adoption rates is high and the probability of a high market adoption rate is low.     

Optimization of risk policy and dividends with fixed transaction costs under interest rate

In this paper, we consider the dividend optimization problem for a financial corporation with transaction costs. Besides the dividend control, the financial corporation takes proportional reinsurance to reduce risk and the surplus earns interest at the constant force ρ>0. Because of the presence of fixed transaction costs, the problem becomes a mixed classical-impulse stochastic control problem. We solve this problem explicitly and construct the value function together with the optimal policy.     

Asymptotic analysis for target asset portfolio allocation with small transaction costs

In this paper we discuss the asset allocation in the presence of small proportional transaction costs. The objective is to keep the asset portfolio close to a target portfolio and at the same time to reduce the trading cost in doing so. We derive the variational inequality and prove a verification theorem. Furthermore, we apply the second order asymptotic expansion method to characterize explicitly the optimal no transaction region when the transaction cost is small and show that the boundary points are asymmetric in relation to the target portfolio position, in contrast to the symmetric relation when only the first order asymptotic expansion method is used, and the leading order is a constant proportion of the cubic root of the small transaction cost. In addition, we use the asymptotic results for the boundary points and obtain an expansion for the value function. The results are illustrated in the numerical example.     

考虑顾客退货和固定成本的联合补货与定价策略

为了吸引更多顾客,许多电子商务零售商允许顾客在一定时间内退货,导致其利润明显减少。同时,在补货时不仅产生依赖补货量的变动成本,而且会产生与补货量无关的固定成本。基于此,以最大化电子商务零售商的利润为目标,建立考虑顾客退货和固定成本的联合补货与定价模型,其中顾客的退货量与满足的需求呈正比。在一般需求情形下,部分刻画多期问题的最优策略;在特殊需求情形下,证明(s,S,p)策略对单期问题最优,并对多期问题的最优策略进行严格刻画。根据已有刻画为多期问题构造启发式策略。数值结果表明启发式策略近似最优;当初始库存水平足够高/低时,最优补货水平和定价随退货率与固定成本单调变化。关键词:联合补货与定价模型;顾客退货;固定成本;随机动态规划;最优策略     

交通拥堵管理中可交易电子券方案的公平性分析

利用损失厌恶理论中的参照依赖模型,构建用户的感知出行成本函数,在固定需求的交通网络中加入电子券交易费用率,建立均衡条件下的变分不等式模型。通过模拟仿真,说明市场交易费用率会影响电子券交易市场,政府可通过调节交易费用率提高电子券方案公平性。选取路网中所有起讫对间出行成本变化率波动的加权平均值,度量可交易电子券方案的公平性,综合考虑最小化系统出行总成本和最大化方案公平性两个目标,构造效用函数,分析不同权重下市场交易费用率对可交易电子券方案的影响,以期对电子券方案的公平性进行优化。