带交易费用的最优投资和比例再保险

研究了保险公司的最优投资和再保险问题.保险公司的盈余通过跳-扩散风险模型来模拟,可以把盈余的一部分投资到金融市场,金融市场由一个无风险资产和n个风险资产组成,并且保险公司还可以购买比例再保险;在买卖风险资产时,考虑了交易费用.通过随机控制的理论,获得了最优策略和值函数的显示解.     

考虑交易费用和债务的再保险和投资问题

该文考虑了保险公司的再保险和投资在多种风险资产中的策略问题. 假设保险公司本身有着一定的债务, 债务的多少服从线性扩散方程. 保险公司可以通过再保险和将再保险之后的剩余资产投资在m种风险资产和一种无风险资产中降低其风险. 资产中风险资产的价格波动服从几何布朗运动, 其债务多少的演化也是依据布朗运动而上下波动. 该文考虑了风险资产与债务之间的相互关系, 考虑了在进行风险投资时的交易费用, 并且利用HJB方程求得保险公司的最大最终资产的预期指数效用, 给出了相应的最优价值函数和最优策略的数值解.     

Optimal Investment and Consumption with Proportional Transaction Costs in Regime-Switching Model

This paper is concerned with an infinite-horizon problem of optimal investment and consumption with proportional transaction costs in continuous-time regime-switching models. An investor distributes his/her wealth between a stock and a bond and consumes at a non-negative rate from the bond account. The market parameters (the interest rate, the appreciation rate, and the volatility rate of the stock) are assumed to depend on a continuous-time Markov chain with a finite number of states (also known as regimes). The objective of the optimization problem is to maximize the expected discounted total utility of consumption. We first show that for a class of hyperbolic absolute risk aversion utility functions, the value function is a viscosity solution of the Hamilton–Jacobi–Bellman equation associated with the optimization problem. We then treat a power utility function and generalize the existing results to the regime-switching case.     

带有交易成本和红利的最优消费投资策略研究

本文利用HJB方程粘性解理论,考虑带有红利收益和交易成本后,对现有最优消费投资模型作了推广,研究了投资者在带有红利和交易成本情形下的最优消费投资策略。     

有交易成本的模糊最优化投资

本文针对交易成本在证券组合投资中的重要地位 ,提出了考虑交易成本 ,并兼顾收益与风险的模糊最优化投资模型 ,分析了交易成本对投资有效边界的影响 ,并给出了最优投资比例公式 .这对投资者进行投资有重要的理论与实践意义 .最后 ,通过释例进行了说明 .     

具有交易成本的证券组合投资决策研究

本文利用均值－方差模型，分析了有交易成本的证券投资组合的决策问题，给出了风险资产和无风险资产的最优投资比例与交易成本关系的一个有意义的结论。     

Optimal Consumption Portfolio and No-Arbitrage with Nonproportional Transaction Costs

In this paper we consider a finite-state financial market with non-proportional transaction cost and bid-ask spreads. The transaction cost consists of two parts: a fixed cost and a proportional cost to the size of transaction. We show that the existence of an optimal consumption policy implies that the market has no strong arbitrage; the opposite, however, is not true, i.e., no strong arbitrage does not imply the existence of an optimal consumption policy. This is in sharp contrast with the case of proportional transaction cost and other cases reported in the literature, where no strong arbitrage is equivalent to the existence of an optimal consumption policy. We also study the relationship between weak arbitrage and strong arbitrage. Different from the market with proportional transaction cost, we find that these two forms of arbitrage are equivalent unless the fixed cost is zero. A necessary and sufficient condition for the existence of an optimal consumption policy is also obtained. Supported by CAS, NSFC, RGC of Hong Kong and NSF under Grant No. DMI-0196084 and DMI-0200306.     

从树型集上最优停止问题到一般偏序集上最优停止问题

本文讨论了树型集上与偏序集上最优停止问题两者间的关系，证明了最优策略与最优控制变量的一一对应关系，从而导出最优策略．可在最优控制变量中取到．     

带交易费的最优投资组合选择的极大极小方法

研究不允许卖空时不相关资产的最优投资选择问题.在风险资产收益率不能确切知道的情况下,建立了投资组合选择问题的极大极小模型.将交易费引入到极大极小模型中,交易费假定为新旧投资组合之差的V型函数.推导出有效投资组合与有效前沿的解析表达式.     

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.     

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We generalize the framework of [18] for optimal stopping time problem to allow a certain restricted class of stopping times. By using classical results in probability theory on families of random variables indexed by a restricted family of stopping times, we prove the existence of an optimal time, givecharacterizations of the minimal and maximal optimal stopping times, and provide some local properties of the value function family, in concert with all special cases studied previously.     

Variational Inequalities in Hilbert Spaces with Measures and Optimal Stopping Problems

We study the existence theory for parabolic variational inequalities in weighted L ² spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L ² setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coefficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.     

Optimal Dividend and Capital Injection Strategies with Transaction Costs and Exponentially Distributed Observation Time

In this paper, we consider the optimal joint dividend and capital injection strategy with proportional and fixed costs. It supposes that capitals can be injected whenever they are profitable, but dividends can only be paid at the arrival times of a Poisson process with intensity . Our objective is to determine an optimal strategy of maximizing the expected cumulative discounted dividends minus the expected discounted costs of capital injections before bankruptcy. By solving some impulse problems, we get the closed-form solutions depending on the parameters of model. Some known results in Lokka and Zervos (2008) can be viewed as limiting cases when .     

有交易成本的投资组合策略

金融市场都存在交易成本,为此,本文建立了有交易成本的投资组合模型,讨论了模型解的条件,并提出模型的通用数值解法,最后给出了应用举例．     

Optimal Design Problems for Two-Phase Conducting Composites with Weakly Discontinuous Objective Functionals

We consider the relatively simple but non-trivial example of an optimal design problem with a weakly discontinuous objective functional. The objective functional is quadratic and was suggested by Tartar in his “Remarks on Optimal Design” paper. We analyze a problem of finding a layout of a conducting composite such that the fields in both phases provide least squares fit to a given field. The main result of the paper is an explicit formula for the relaxed optimal design problem, suitable for numerical solution. Further analysis of our explicit formula shows that the optimal layout is a rank one laminate locally, lending some support for Tartar's conjecture that the minimizing sequences always converge strongly.     

Approximately Multiplicative Functionals on Algebras of Smooth Functions

Let be a bounded linear functional on A, where A is a commutativeBanach algebra, then the bilinear functional is defined as (a,b)= (ab)- (a) (b) for each a and b in A. If the norm of is small then is approximatelymultiplicative, and it is of interest whether or not |||| being small implies that is nearto a multiplicative functional. If this property holds for acommutative Banach algebra then A is an AMNM algebra (approximatelymultiplicative functionals are near multiplicative functionals).The main result of the paper shows that C^N [0,1]^M (the complexvalued functions defined on [0,1]^M with all Nth order partialderivatives continuous) is AMNM. It is also shown that a similarproof can be applied to certain Lipschitz algebras.     

一类投资时点问题的最优停止模型及其等待时间

针对收益流与一次性投入沉淀成本均不确定的一类风险项目,为使其预期总的贴现净收益最大,提出了寻找项目最优投资时点的最优停止模型.这种方法不依赖于金融市场的完备性及市场无套利.借助于高切原理,通过求解一个自由边界问题,得到模型的候选解.运用最优停止理论证明了其的确为最优解,从而显式地给出了该类风险项目的最优投资时点.进一步,显式给出了到达最优时点的平均等待时间.     

Portfolio Optimization Model with Transaction Costs

Abstract The purpose of the article is to formulate,under the l_∞ risk measure,a model of portfolio selectionwith transaction costs and then investigate the optimal strategy within the proposed.The characterization of aoptimal strategy and the efficient algorithm for finding the optimal strategy are given.