机构投资者的最优变现策略

在投资、变现等大宗交易过程中,资产交易价格与交易策略密切相关,因此,交易的完成过程需要很高的技巧.文章讨论了机构投资者的最优变现策略问题,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,得到了最优变现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:最优变现策略与瞬时冲击、市场波动率及风险厌恶系数等参数有关,但与永久冲击无关,且最优变现策略对市场波动率和瞬时冲击的变化较敏感.     

Ho-Lee利率模型下多种风险资产的动态投资组合

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。     

Lévy模型下的最优寿险、消费和投资

利用最小最大鞅测度方法研究了一个具有不确定寿命的有工资收入者(职员)所面临的最优寿险消费投资问题.金融市场由一种无风险资产和一种风险资产组成,风险资产价格动态由指数Lévy过程刻画.工资所有者的目标是期望效用最大化.基于最小最大鞅测度,该文得到了各种效用函数下最优策略的显式解,并通过数值模拟讨论了参数对最优策略的影响.     

Heston随机波动率模型下的动态投资组合

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.     

状态相依效用下的超额损失再保险-投资策略

假设保险公司的盈余过程和金融市场的资产价格过程均由可观测的连续时间马尔科夫链所调节,以最大化终端财富的状态相依的期望指数效用为目标,研究了保险公司的超额损失再保险-投资问题.运用动态规划方法,得到最优再保险-投资策略的解析解以及最优值函数的半解析式.最后,通过数值例子,分析了模型各参数对最优值函数和最优策略的影响.     

两类相依保险业务下基于竞争的最优再保险策略

在再保险合同制定中,保险公司与再保险公司之间是竞争的.利用相对业绩,本文量化了这种竞争.进而假设保险公司从事两类相依保险业务,在竞争下,得到了保险公司的相对财富过程.保险公司的目标是,寻找最优时间一致的再保险策略最大化终端财富的均值同时最小化其方差.通过使用随机分析和随机控制理论,求得了最优时间一致的再保险策略和值函数的显式解,并从理论方面解释了最优解的保险和经济意义.最终,通过数值实验分析了模型参数对最优时间一致再保险策略的影响,比较了两类特殊情形与一般情形下最优再保险策略之间的关系.通过本文的研究得到了一些新的发现,研究结果可以更合理地指导保险公司的再保险决策.     

考虑模型不确定的TBP养老金的鲁棒最优投资策略研究

以目标收益养老金计划(TBP)模型研究鲁棒最优投资问题, 其中养老金管理者对模型参数不确定带来的风险是模糊风险厌恶的. 养老金管理者为规避风险和增加收益将投资于无风险资产和风险资产. 考虑连续时间情形, 假设养老金计划参保人的缴费是确定的, 而参保人的收益给付是确定目标收益给付, 资金账户的收益风险由不同代际的参保人共同承担, 同时考虑随机工资及其与金融市场的相关性. 以参保人退休后养老金给付偏离目标的风险和代际之间风险分担的组合最小化为投资决策目标, 并采用指数函数的形式描述实际给付与目标给付的偏离, 利用随机最优控制方法, 建立相应的HJB方程并求解得到最优投资收益策略和最优给付策略的解析解. 通过数值示例分析了模型参数对最优投资和最优给付策略的影响.     

Vasicek利率模型下带有零息票债券的投资-消费模型

应用随机最优控制理论研究Vasicek利率模型下的投资-消费问题,其中假设无风险利率是服从Vasicek利率模型的随机过程,且与股票价格过程存在一般相关性.假设金融市场由一种无风险资产、一种风险资产和一种零息票债券所构成,投资者的目标是最大化中期消费与终端财富的期望贴现效用.应用变量替换方法得到了幂效用下最优投资-消费策略的显示表达式,并分析了最优投资-消费策略对市场参数的灵敏度.     

随机需求下具有有效期的易变质物品的库存管理北大核心CSCD

本本文研究了无限时间具有有效期的易变质物品的(T,r,Q)的库存补货策略.在市场需求率随机,允许缺货且设定最大缺货量的条件下,建立了一个确定易变质物品最优补货策略的优化模型,并采用缺货回补的办法,利用多元极值和隐函数定理的思想得到了最优补货批量和订货点.在最后的算例中,通过Matlab软件模拟出最优补货批量和最优缺货量,并对模型的参数作了灵敏性分析.     

Vasicek利率与Heston模型下的最优投资和再保险

本文主要研究Vasicek随机利率模型下保险公司的最优投资与再保险问题.假设保险公司的盈余过程由带漂移的布朗运动来描述,保险公司通过购买比例再保险来转移索赔风险;同时,将财富投资于由一种无风险资产与一种风险资产组成的金融市场,其中,利率期限结构服从Vasicek利率模型,且风险资产价格过程满足Heston随机波动率模型.利用动态规划原理及变量替换的方法,得到了指数效用下最优投资与再保险策略的显示表达式,并给出数值例子分析了主要模型参数对最优策略的影响.     

Model-adaptive optimal discretization of stochastic integrals*

We study the optimal discretization error of stochastic integrals driven by a multidimensional continuous Brownian semimartingale. In the previous works a pathwise lower bound for the renormalized quadratic variation of the error was provided together with an asymptotically optimal discretization strategy, i.e. for which the lower bound is attained. However the construction of the optimal strategy involved the knowledge about the diffusion coefficient of the semimartingaleunder study. In this work we provide a model-adaptive asymptotically optimal discretization strategy that does not require any prior knowledge about the model. We prove the optimality for quite general class of discretization strategies based on kernel techniques for adaptive estimation and previously obtained optimal strategies that use random ellipsoid hitting times.     

Marketing Strategy Formulation — Pure versus Mixed Strategies

The paper considers Kotler's competitive model and increases the number of possible marketing strategies available by taking into account the combinations of the strategy alternatives. From the larger set of marketing strategies, the optimal strategy or strategies is identified. The objective function of the firm is found to be satisfied better by the combined strategy rather than by the best strategy from the set used by Kotler. The optimal combined strategy is found by a heuristically optimizing SDRDYN-algorithm suitable to simulation studies. As is expected, the larger set of strategy alternatives considered enable the firm to increase the value of its objective function.     

常数比例投资组合保险(CPPI)策略 --捐赠型基金投资策略的最优选择

本文采用Merton提出的处理捐赠型基金的连续时间模型的一般框架，分析了在风险资产为几何布朗运动，效用函数为CRRA效用函数，且捐赠型基金有动态最低支出时的最优支出策略和最优投资策略，结果表明存在一条策略基准线，当基金的总资产在策略基准线之上时，基金管理人关于基金支出与投资策略的选择与不存在最低支出的要求时所作出的决策是一样的，但是一旦基金的总资产低于这条策略基准线时，基金管理人便需要考虑到基金将来必要的支出，并实际影响到他对投资策略的选择，此时基金管理人可作的最优选择是：最低的支出和一种为复制幂收益函数期权的CPPI投资策略。     

Pre-commitment vs. time-consistent strategies for the generalized multi-period portfolio optimization with stochastic cash flows

In this paper, we propose a multi-period portfolio optimization model with stochastic cash flows. Under the mean–variance preference, we derive the pre-commitment and time-consistent investment strategies by applying the embedding scheme and backward induction approach, respectively. We show that the time-consistent strategy is identical to the optimal open-loop strategy. Also, under the exponential utility preference, we develop the optimal strategy for multi-period investment, which is time-consistent. We show that the above two time-consistent strategies are equivalent in some cases. We compare the pre-commitment and time-consistent strategies under different situations with some numerical simulations. The results indicate that the time-consistent strategy is more stable and secure than pre-commitment strategy under the generalized mean–variance criterion.     

The Optimal Control of a Train

We consider the problem of determining an optimal driving strategy in a train control problem with a generalised equation of motion. We assume that the journey must be completed within a given time and seek a strategy that minimises fuel consumption. On the one hand we consider the case where continuous control can be used and on the other hand we consider the case where only discrete control is available. We pay particular attention to a unified development of the two cases. For the continuous control problem we use the Pontryagin principle to find necessary conditions on an optimal strategy and show that these conditions yield key equations that determine the optimal switching points. In the discrete control problem, which is the typical situation with diesel-electric locomotives, we show that for each fixed control sequence the cost of fuel can be minimised by finding the optimal switching times. The corresponding strategies are called strategies of optimal type and in this case we use the Kuhn–Tucker equations to find key equations that determine the optimal switching times. We note that the strategies of optimal type can be used to approximate as closely as we please the optimal strategy obtained using continuous control and we present two new derivations of the key equations. We illustrate our general remarks by reference to a typical train control problem.     

Discrete time market with serial correlations and optimal myopic strategies

The paper studies discrete time market models with serial correlations. We found a market structure that ensures that the optimal strategy is myopic for the case of both power or log utility function. In addition, discrete time approximation of optimal continuous time strategies for diffusion market is analyzed. It is found that the performance of optimal myopic diffusion strategies cannot be approximated by optimal strategies with discrete time transactions that are optimal for the related discrete time market model.     

A pursuit and evasion problem with measurement uncertainty

A pursuit-evasion process with uncertain state-dependent measurements, in finite, discrete time and in a finite, discrete state space, is considered. Three types of strategies which might be employed in such a process are compared, and attention is concentrated on the behavior strategy, the least well known of the three types, but often the simplest optimal strategy to employ.A variation of the Brown-Robinson fictitious play algorithm is presented which can be used to compute behavior strategies in the case of perfect recall processes.Two examples are given in which optimal behavior strategies are computed using the algorithm and compared with a type of plausible but nonoptimalseparation strategy.This work was partially supported by NASA Grant No. NGR-15-005-021, NSF Grant No. GK-1970, and AFOSR Grant No. 69-1776.     

考虑地位效应时炫耀性虚拟商品的最优定价与普及版本化

考虑地位效应的影响,针对炫耀性虚拟商品,决策最优定价和普及版本化。建立了单标准版策略、双版本免费普及策略和双版本销售策略等三种模型,求解得到企业在对应策略下对单版本或双版本的炫耀性虚拟商品的最优定价,在此基础上分析得到地位效应对虚拟商品价格、企业利润和最优普及版本化策略的影响。研究发现地位效应是导致标准版炫耀性虚拟商品价格和企业利润提升的因素;当存在地位效应时,双版本销售策略是炫耀性虚拟商品的最优普及版本化策略;但双版本销售策略相比于单标准版策略的优势在一定条件下因网络外部性增强而削弱。