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1.
讨论了机构投资者的最优持仓策略问题,假设证券价格服从几何布朗运动,以均值方差效用为目标函数,得到了最优持仓策略所满足的二阶微分方程,并由差分法得到其数值解.最后,由参数的敏感性分析知:最优持仓策略与瞬时冲击、市场波动率及风险厌恶系数等参数有关,并分析了参数变化对最优持仓策略的影响.  相似文献   

2.
引入信息不对称和瞬时冲击,研究了捕食交易策略及其存在的必要条件,并给出数值算例.结论表明,捕食者的最优交易策略为时间的二次曲线形式,并且捕食交易利润是瞬时冲击系数的单调减函数.  相似文献   

3.
假设无风险利率可由Ho-Lee利率模型描述,且与股票动态存在一般线性相关系数,应用最优性原理和HJB方程研究了市场存在多种风险资产情形的动态资产分配问题,通过变量替换方法得到了幂效用和指数效用下最优投资策略的显示解,数值算例分析了利率参数和市场参数对最优投资策略的影响趋势。研究结果发现:两种效用下的最优策略均由两部分所构成,一部分由市场参数所确定,另一部分由利率参数所确定。而且,幂效用下的最优投资策略与瞬时利率无关,而指数效用下的最优投资策略与瞬时利率相关。  相似文献   

4.
常浩 《经济数学》2013,30(2):48-54
应用随机最优控制方法对Heston随机波动率模型下的动态投资组合问题进行了研究,得到了幂效用和指数效用下最优投资策略的显示解,并给出一些数值计算结果分析了市场参数对最优投资策略的影响.  相似文献   

5.
考虑现实市场中红利的存在、波动率等参数随时间变化以及交易时间不连续产生的对冲风险不可忽略,研究离散时间、支付红利条件下基于混合规避策略的期权定价模型.由平均自融资-极小方差规避策略得到相应欧式看涨期权定价方程,并且分别使用偏微分方法和概率论方法得到统一的闭形解.数值分析表明,与经典的期权定价模型相比,新模型中的期权价格更接近对冲成本.  相似文献   

6.
本文研究了随机波动率市场中存在股票误价(mispricing)时的最优投资组合选择问题.假设投资者的目标是最大化终端财富的期望幂效用;其可投资于无风险资产、市场指数和两支相同权益或近似度极高的股票,其中至少有一支股票存在误价;市场收益的波动率和股票系统风险由Heston随机波动率模型刻画.运用动态规划方法和Lagrange乘子法,分别得到不存在/存在有限卖空约束时,投资者的最优投资策略及最优值函数的解析式,并通过理论分析和数值算例,阐述了投资时间水平和价格随机误差对最优投资策略的影响.  相似文献   

7.
研究了Heston随机波动率模型下带有负债过程的动态投资组合问题,并且假设风险资产价格过程满足Heston随机波动率模型,负债过程服从带漂移的布朗运动.金融市场由一种无风险资产和一种风险资产所构成.首先,应用动态规划原理得到相应值函数所满足的HJB方程.然后,假设投资者对风险的偏好程度满足双曲绝对风险厌恶(HARA)效用函数,并应用Legendre变换法和分离变量法得到在HARA效用函数下最优投资策略的显示解.最后,给出数值算例分析部分市场参数对最优投资策略的影响.  相似文献   

8.
应用随机最优控制方法研究Heston随机波动率模型下带有负债过程的动态投资组合问题,其中假设股票价格服从Heston随机波动率模型,负债过程由带漂移的布朗运动所驱动.金融市场由一种无风险资产和一种风险资产组成.应用随机动态规划原理和变量替换法得出了上述问题在幂效用和指数效用函数下最优投资策略的显示解,并给出数值算例分别分析了市场参数在幂效用和指数效用函数下对最优投资策略的影响.  相似文献   

9.
研究了马尔可夫机制转换模型下确定缴费型养老金计划的最优投资问题.假定市场中风险资产价格与企业员工的工资都满足马尔可夫调制的几何布朗运动模型,它们的预期回报率和波动率都依赖于市场经济状态,其经济状态由一连续时间马尔可夫链来描述.利用最终财富的最大期望效用准则,得到了养老金管理者的最优投资策略,结果表明市场的经济状态对最优投资策略有着很大的影响.最后通过数值计算分析了市场利率和绝对风险厌恶系数与最优投资策略的关系.  相似文献   

10.
研究存在模型风险的最优投资决策问题,将该问题刻画为投资者与自然之间的二人-零和随机微分博弈,其中自然是博弈的"虚拟"参与者.利用随机微分博弈分析方法,通过求解最优控制问题对应的HJBI(Hamilton-Jacobi-Bellman-Isaacs)方程,在完备市场和存在随机收益流的非完备市场模型下,都得到了投资者最优投资策略以及最优值函数的解析表达式.结果表明,在完备市场条件下,投资者的最优风险投资额为零,在非完备市场条件下最优投资策略将卖空风险资产,且卖空额随着随机收益流波动率的增大而增加,随风险资产波动率增大而减少.  相似文献   

11.
In this paper, we develop optimal trading strategies for a risk averse investor by minimizing the expected cost and the risk of execution. Here we consider a law of motion for price which uses a convex combination of temporary and permanent market impact. In the special case of unconstrained problem for a risk neutral investor, we obtain a closed form solution for optimal trading strategies by using dynamic programming. For a general problem, we use a quadratic programming approach to get approximate dynamic optimal trading strategies. Further, numerical examples of optimal execution strategies are provided for illustration purposes.  相似文献   

12.
Abstract

The author considers the dynamic trading strategies that minimize the expected cost of trading a large block of securities over a fixed finite number of periods. In this model, the market impact function that yields the execution prices for individual trades is endogeneously determined. This analysis is novel in that it introduces small investors, who do not affect the price flow, and a noise trader as market participants other than the institutional investors into a general equilibrium model. It is found that the institutional investor takes a rather complicated strategy to make use of its private information. As a result, the price impact not only changes over time but also depends on the trade history. Although there are several studies that deal with this topic in the recent empirical literature, it has remained unnoticed in the context of the theoretical optimal execution model.  相似文献   

13.
Abstract

Electronic trading of equities and other securities makes heavy use of ‘arrival price’ algorithms that balance the market impact cost of rapid execution against the volatility risk of slow execution. In the standard formulation, mean–variance optimal trading strategies are static: they do not modify the execution speed in response to price motions observed during trading. We show that substantial improvement is possible by using dynamic trading strategies and that the improvement is larger for large initial positions.

We develop a technique for computing optimal dynamic strategies to any desired degree of precision. The asset price process is observed on a discrete tree with an arbitrary number of levels. We introduce a novel dynamic programming technique in which the control variables are not only the shares traded at each time step but also the maximum expected cost for the remainder of the program; the value function is the variance of the remaining program. The resulting adaptive strategies are ‘aggressive-in-the-money’: they accelerate the execution when the price moves in the trader's favor, spending parts of the trading gains to reduce risk.  相似文献   

14.
In this article, we take an algorithmic approach to solve the problem of optimal execution under time-varying constraints on the depth of a limit order book (LOB). Our algorithms are within the resilience model proposed by Obizhaeva and Wang (2013) with a more realistic assumption on the order book depth; the amount of liquidity provided by an LOB market is finite at all times. For the simplest case where the order book depth stays at a fixed level for the entire trading horizon, we reduce the optimal execution problem into a one-dimensional root-finding problem which can be readily solved by standard numerical algorithms. When the depth of the order book is monotone in time, we apply the Karush-Kuhn-Tucker conditions to narrow down the set of candidate strategies. Then, we use a dichotomy-based search algorithm to pin down the optimal one. For the general case, we start from the optimal strategy subject to no liquidity constraints and iterate over execution strategy by sequentially adding more constraints to the problem in a specific fashion until primal feasibility is achieved. Numerical experiments indicate that our algorithms give comparable results to those of current existing convex optimization toolbox CVXOPT with significantly lower time complexity.  相似文献   

15.
The efficient modeling of execution price path of an asset to be traded is an important aspect of the optimal trading problem. In this paper an execution price path based on the second order autoregressive process is proposed. The proposed price path is a generalization of the existing first order autoregressive price path in literature. Using dynamic programming method the analytical closed form solution of unconstrained optimal trading problem under the second order autoregressive process is derived. However in order to incorporate non-negativity constraints in the problem formulation, the optimal static trading problems under second order autoregressive price process are formulated. For a risk neutral investor, the optimal static trading problem of minimizing expected execution cost subject to non-negativity constraints is formulated as a quadratic programming problem. Whereas, for a risk averse investor the variance of execution cost is considered as a measure for the timing risk, and the mean–variance problem is formulated. Moreover, the optimal static trading problem subject to stochastic dominance constraints with mean–variance static trading strategy as the reference strategy is studied. Using Static approximation method the algorithm to solve proposed optimal static trading problems is presented. With numerical illustrations conducted on simulated data and the real market data, the significance of second order autoregressive price path, and the optimal static trading problems is presented.  相似文献   

16.
Atomic Orders are the basic elements of any algorithm for automated trading in electronic stock exchanges. The main concern in their execution is achieving the most efficient price. We propose two optimal strategies for the execution of atomic orders based on minimization of impact and volatility costs. The first considered strategy is based on a relatively simple nonlinear optimization model while the second allows re-optimization at some time point within a given execution time. In both cases a combination of market and limit orders is used. The key innovation in our approach is the introduction of a Fill Probability function which allows a combination of market and limit orders in the two optimization models we are discussing in this paper. Under certain conditions the objective functions of both considered problems are convex and therefore standard optimization tools can be applied. The efficiency of the resulting strategies is tested against two benchmarks representing common market practice on a representative sample of real trading data.  相似文献   

17.
Arti Singh 《Optimization》2017,66(11):1931-1951
Abstract

In this paper, an optimal portfolio execution problem under price model which exhibits cointegration behaviour is proposed. The proposed problem is formulated as a quadratic programming problem. With different statistical procedures and parameter estimation methods, employed on real market financial data, the four portfolios are constructed with which, computational study is performed. It is shown that the trading strategies constructed out of portfolios with cointegrated price dynamics show significant reduction in execution cost.  相似文献   

18.
The optimal trade execution problem is formulated in terms of a mean-variance tradeoff, as seen at the initial time. The mean-variance problem can be embedded in a linear-quadratic (LQ) optimal stochastic control problem. A semi-Lagrangian scheme is used to solve the resulting nonlinear Hamilton-Jacobi-Bellman (HJB) PDE. This method is essentially independent of the form for the price impact functions. Provided a strong comparison property holds, we prove that the numerical scheme converges to the viscosity solution of the HJB PDE. Numerical examples are presented in terms of the efficient trading frontier and the trading strategy. The numerical results indicate that in some cases there are many different trading strategies which generate almost identical efficient frontiers.  相似文献   

19.
We provide an explicit closed-form strategy for an investor who executes a large order when market order-flow from all agents, including the investor’s own trades, has a permanent price impact. The strategy is found in closed-form when the permanent and temporary price impacts are linear in the market’s and investor’s rates of trading. We do this under very general assumptions about the stochastic process followed by the order-flow of the market. The optimal strategy consists of an Almgren–Chriss execution strategy adjusted by a weighted-average of the future expected net order-flow (given by the difference of the market’s rate of buy and sell market orders) over the execution trading horizon and proportional to the ratio of permanent to temporary linear impacts. We use historical data to calibrate the model to Nasdaq traded stocks and use simulations to show how the strategy performs.  相似文献   

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