On the construction of non-affine jump-diffusion models

We describe a method for construction of jump analogues of certain one-dimensional diffusion processes satisfying solvable stochastic differential equations. The method is based on the reduction of the original stochastic differential equations to the ones with linear diffusion coefficients, which are reducible to the associated ordinary differential equations, by using the appropriate integrating factor processes. The analogues are constructed by means of adding the jump components linearly into the reduced stochastic differential equations. We illustrate the method by constructing jump analogues of several diffusion processes and expand the notion of market price of risk to the resulting non-affine jump-diffusion models.     

Utility maximization problem with random endowment and transaction costs: when wealth may become negative

In this article, we study the problem of maximizing expected utility from the terminal wealth with proportional transaction costs and random endowment. In the context of the existence of consistent price systems, we consider the duality between the primal utility maximization problem and the dual one, which is set up on the domain of finitely additive measures. In particular, we prove duality results for utility functions supporting possibly negative values. Moreover, we construct a shadow market by the dual optimal process and consider the utility-based pricing for random endowment.     

粮食最低收购价政策问题研究

利用聚类分析、逐步回归分析确定小麦与稻谷种植面积模型和指标体系.建立综合指标评价模型和ARMA模型,可知:最低收购政策具有托市效应.结合时间趋势剔除法、蛛网模型,可知:小麦和稻谷价格波动呈现5、3年的周期性,分别满足发散型、收敛型蛛网形态.建立基于补偿法的最低收购价定价模型并用BP神经网络模型进行检验.基于反证法,推知调控最低收购价提高5%小麦种植面积的做法是不可行的.最后提出了调控粮食种植的建议·     

基于面板模型的商品房价格影响因素的实证研究

选取了我国30个省市2006~2015年的面板数据,应用面板数据计量模型回归的方法,基于R语言对影响商品房价格的因素进行实证研究.首先,经过Hausman检验与F检验确定面板数据的模型为混合估计模型;模型可以通过十折交叉验证法、残差正太性的检验、Q-Q图检验、变量间共线性的检验;最后经过逐步回归分析,结果表明土地价格、商品房销售面积、居民可支配收入、人均国内总产值财政收入占地区生产总值比重、汇率这6个指标对商品房价格都有显著性的影响.其中,土地价格和居民可支配收入对商品房价格的影响最为突出.     

On the Existence Of Consistent Price Systems

We formulate a sufficient condition for the existence of a consistent price system (CPS), which is weaker than the conditional full support condition (CFS). We use the new condition to show the existence of CPSs for certain processes that fail to have the CFS property. In particular this condition gives sufficient conditions, under which a continuous function of a process with CFS admits a CPS, while the CFS property might be lost.     

A non-Gaussian Ornstein–Uhlenbeck model for pricing wind power futures

The recent introduction of wind power futures written on the German wind power production index has brought with it new interesting challenges in terms of modelling and pricing. Some particularities of this product are the strong seasonal component embedded in the underlying, the fact that the wind index is bounded from both above and below and also that the futures are settled against a synthetically generated spot index. Here, we consider the non-Gaussian Ornstein–Uhlenbeck type processes proposed by Barndorff-Nielsen and Shephard in the context of modelling the wind power production index. We discuss the properties of the model and estimation of the model parameters. Further, the model allows for an analytical formula for pricing wind power futures. We provide an empirical study, where the model is calibrated to 37 years of German wind power production index that is synthetically generated assuming a constant level of installed capacity. Also, based on 1 year of observed prices for wind power futures with different delivery periods, we study the market price of risk. Generally, we find a negative risk premium whose magnitude decreases as the length of the delivery period increases. To further demonstrate the benefits of our proposed model, we address the pricing of European options written on wind power futures, which can be achieved through Fourier techniques.     

Separation between second price auctions with personalized reserves and the revenue optimal auction

When buyer valuations are drawn IID from a known regular distribution, a second price auction with a symmetric reserve price is the revenue-optimal single-item auction. When this distribution is irregular, we provide the first separation result showing that a second price auction with reserves earns at most 0.778 times the revenue of Myerson’s optimal auction, even when the reserves can be asymmetric. Since the lower bound is 0.745 for i.i.d. buyers, our result is nearly tight.     

Statistical inference and modelling of momentum in stock prices

The following results are obtained, (i) It is possible to obtain a time series of market data {y(t)} in which the fluctuations in fundamental value have been compensated for. An objective test of the efficient market hypothesis (EMH), which would predict random correlations about a constant value, is thereby possible, (ii) A time series procedure can be used to determine the extent to which the differences in the data and the moving averages are significant. This provides a model of the form y(t)-y(t-l)=0.5{y(t- l)-y(t-2)}+ε(t)+0.8ε(r-1) where ε(t) is the error at time t, and the coefficients 0.5 and 0.8 are determined from the data. One concludes that today's price is not a random perturbation from yesterday's; rather, yesterday's rate of change is a significant predictor of today's rate of change. This confirms the concept of momentum that is crucial to market participants. (iii) The model provides out-of-sample predictions that can be tested statistically. (iv) The model and coefficients obtained in this way can be used to make predictions on laboratory experiments to establish an objective and quantitative link between the experiments and the market data. These methods circumvent the central difficulty in testing market data, namely, that changes in fundamentals obscure intrinsic trends and autocorrelations. This procedure is implemented by considering the ratio of two similar funds (Germany and Future Germany) with the same manager and performing a set of statistical tests that have excluded fluctuations in fundamental factors. For the entire data of the first 1149 days beginning with the introduction of the latter fund, a standard runs test indicates that the data is 29 standard deviations away from that which would be expected under a hypothesis of random fluctuations about the fundamental value. This and other tests provide strong evidence against the efficient market hypothesis and in favour of autocorrelations in the data. An ARIMA time series finds strong evidence (9.6 and 21.6 standard deviations in the two coefficients) that the data is described by a model that involves the first difference, indicating that momentum is the significant factor. The first quarter's data is used to make out-of-sample predictions for the second quarter with results that are significant to 3 standard deviations. Finally, the ARIMA model and coefficients are used to make predictions on laboratory experiments of Porter and Smith in which the intrinsic value is clear. The model's forecasts are decidedly more accurate than that of the null hypothesis of random fluctuations about the fundamental value.     

Contract type and decision right of sales promotion in supply chain management with a capital constrained retailer

From the practices of Chinese consumer electronics market, we find there are two key issues in supply chain management: The first issue is the contract type of either wholesale price contracts or consignment contracts with revenue sharing, and the second issue is the decision right of sales promotion (such as advertising, on-site shopping assistance, rebates, and post-sales service) owned by either manufacturers or retailers. We model a supply chain with one manufacturer and one retailer who has limited capital and faces deterministic demand depending on retail price and sales promotion. The two issues interact with each other. We show that only the combination (called as chain business mode) of a consignment contract with the manufacturer’s right of sales promotion or a wholesale price contract with the retailer’s right of sales promotion is better for both members. Moreover, the latter chain business mode is realized only when the retailer has more power in the chain and has enough capital, otherwise the former one is realized. But which one is preferred by customers? We find that the former is preferred by customers who mainly enjoy low price, while the latter is preferred by those who enjoy high sales promotion level.     

Real-World Forward Rate Dynamics With Affine Realizations

We investigate the existence of affine realizations for Lévy driven interest rate term structure models under the real-world probability measure, which so far has only been studied under an assumed risk-neutral probability measure. For models driven by Wiener processes, all results obtained under the risk-neutral approach concerning the existence of affine realizations are transferred to the general case. A similar result holds true for models driven by compound Poisson processes with finite jump size distributions. However, in the presence of jumps with infinite activity we obtain severe restrictions on the structure of the market price of risk; typically, it must even be constant.