ROBUST UTILITY MAXIMIZATION WITH LÉVY PROCESSES

We study a robust portfolio optimization problem under model uncertainty for an investor with logarithmic or power utility. The uncertainty is specified by a set of possible Lévy triplets, that is, possible instantaneous drift, volatility, and jump characteristics of the price process. We show that an optimal investment strategy exists and compute it in semi‐closed form. Moreover, we provide a saddle point analysis describing a worst‐case model.     

Popular Urbanization: Conceptualizing Urbanization Processes Beyond Informality

This article introduces the concept of popular urbanization to describe a specific urbanization process based on collective initiatives, self-organization and the activities of inhabitants. We understand popular urbanization as an urban strategy through which an urban territory is produced, transformed and appropriated by the people. This concept results from a theoretically guided and empirically grounded comparison of Mexico City, Istanbul and Lagos. Based on postcolonial critiques of urban theory and on the epistemologies of planetary urbanization, we bring urbanization processes in these urban regions into conversation with each other through a multidimensional theoretical framework inspired by Henri Lefebvre focusing on material interaction, territorial regulation, and everyday experience. In this way, popular urbanization emerged as a distinct urbanization process, which we identified in all three contexts. While this process is often subsumed under the broader concept of ‘urban informality’, we suggest that it may be helpful to distinguish popular urbanization as primarily led by the people, while commodification and state agencies play minor roles. As popular urbanization unfolds in diverse ways dependent upon the wider urban context, specific political constellations and actions, it results in a variety of spatial outcomes and temporal trajectories. This is therefore a revisable and open concept. In proposing the concept of popular urbanization for further examination, we seek to contribute to the collective development of a decentered vocabulary of urbanization.     

On peacocks and lyrebirds: Australian options,Brownian bridges,and the average of submartingales

We introduce a class of stochastic processes, which we refer to as lyrebirds. These extend a class of stochastic processes, which have recently been coined peacocks, but are more commonly known as processes that are increasing in the convex order. We show how these processes arise naturally in the context of Asian and Australian options and consider further applications, such as the arithmetic average of a Brownian bridge and the average of submartingales, including the case of Asian and Australian options where the underlying features constant elasticity of variance or is of Merton jump diffusion type.     

MULTIVARIATE STABLE FUTURES PRICES

This paper introduces new techniques for modeling financial data under the assumption that the data belong to the domain of attraction of a multivariate stable Pareto law. We provide tail estimators for the index of stability parameter a and the corresponding spectral measure. These estimators are then applied to test the associtation of the individual components and to compute estimates of portfolio risk and the covariation of commodities. A practical example is given using DM-dollar and JY-dollar exchange rates data.     

Optimal Sure Portfolio Plans

This paper is a sequel to the author's "Certainty Equivalence in the Continuous-Time Portfolio-cum-Saving Model" in Applied Stochastic Analysis (eds. M. H. A. Davis and R. J. Elliot), where a model of optimal accumulation of capital and portfolio choice over an infinite horizon in continuous time was considered in which the vector process representing returns to investment is a general semimartingale with independent increments and the welfare functional has the discounted constant relative risk aversion (CRRA) form. A problem of optimal choice of a sure (i.e., nonrandom portfolio plan can be defined in such a way that solutions of this problem correspond to solutions of optimal choice of a portfolio-cum-saving plan, provided that the distant future is sufficiently discounted. This has been proved in the earlier paper, and is in part proved again here by different methods. Using the canonical representation of a PII-semimartingale, a formula of Lévy-Khinchin type is derived for the bilateral Laplace transform of the compound interest process generated by a sure portfolio plan. With its aid. the existence of an optimal sure portfolio plan is proved under suitable conditions, and various causes of nonexistence are identified. Programming conditions characterizing an optimal sure portfolio plan are also obtained.     

Parametric continuity of stationary distributions

For Markovian economic models, long-run equilibria are typically identified with the stationary (invariant) distributions generated by the model. In this paper we provide new sufficient conditions for continuity in the map from parameters to these equilibria. Several existing results are shown to be special cases of our theorem. This paper has benefitted from the helpful comments of Kevin Reffett, Rabee Tourky, an anonymous referee and participants at the 13th European Workshop on General Equilibrium Theory, Venice 2004. The second author is grateful for financial support from Australian Research Council Grant DP0557625.     

美元指数与原油价格暴涨暴跌的交互刺激研究

采用具有相互刺激特征的Hawkes过程探究美元指数与原油价格暴涨暴跌的交互刺激作用。结果表明:在暴涨暴跌幅度均服从广义帕累托分布的基础上, Hawkes过程对美元指数与原油价格的暴涨暴跌均拟合得较好;美元指数和原油价格的暴涨暴跌具有明显的自我刺激效应,且原油价格的暴涨暴跌会单向刺激美元指数暴涨暴跌的发生,即交叉刺激效应具有非对称性。同时,实证发现Hawkes过程对美元指数与原油价格的暴涨暴跌的预测能力要优于泊松过程。     

COS method for option pricing under a regime-switching model with time-changed Lévy processes

We extend the regime-switching model to the rich class of time-changed Lévy processes and use the Fourier cosine expansion (COS) method to price several options under the resulting models. The extension of the COS method to price under the regime-switching model is not straightforward because it requires the evaluation of the characteristic function which is based on a matrix exponentiation which is not an easy task. For a two-state economy, we give an analytical expression for computing this matrix exponential, and for more than two states, we use the Carathéodory–Fejér approximation to find the option prices efficiently. In the new framework developed here, it is possible to allow switches not only in the model parameters as is commonly done in literature, but we can also completely switch among various popular financial models under different regimes without any additional computational cost. Calibration of the different regime-switching models with real market data shows that the best models are the regime-switching time-changed Lévy models. As expected by the error analysis, the COS method converges exponentially and thus outperforms all other numerical methods that have been proposed so far.     

Transform analysis for Hawkes processes with applications in dark pool trading

Hawkes processes are a class of simple point processes that are self-exciting and have a clustering effect, with wide applications in finance, social networks and many other fields. This paper considers a self-exciting Hawkes process where the baseline intensity is time-dependent, the exciting function is a general function and the jump sizes of the intensity process are independent and identically distributed nonnegative random variables. This Hawkes model is non-Markovian in general. We obtain closed-form formulas for the Laplace transform, moments and the distribution of the Hawkes process. To illustrate the applications of our results, we use the Hawkes process to model the clustered arrival of trades in a dark pool and analyse various performance metrics including time-to-first-fill, time-to-complete-fill and the expected fill rate of a resting dark order.     

The pyramid model of school management

Models of organizational management are presented in the literature and in the managerial practices of recent years. They are aimed to improve organizational governance, and to enhance organizational overall efficiency. The common denominator for most, if not all these management models is that they generally focus on a single aspect, or on a very limited number of aspects of the organizational conduct whereas running an organization is a highly complex undertaking, incorporating a large number of functions and processes. School principals tend to adapt out-of-school management process, usually adapting them from the business world. And therefore we can see that the educational system at all and the school system in particular, implement business management methods. This research indicates that school principals are well aware of all the school management processes and procedures. The important contribution of this research, which is based on the unique contribution of the multi-faceted theory, is acknowledging the work of the school principals as a pyramid which its base is composed of essential consensus procedures and its three sided indicate three major school management process. We suggest that this pyramid will be called “The Pyramid Model of School Management”. The various management processes that built this pyramid are based on mutual aims and consensus of the school team to reach these aims. The consensus of the aims is essential, and with out it, the school cannot exist as an affective organization. Choosing when to take a various management action is a feedback based, and situation-based conduct. It is also shown in this research that school principals distinguish between three major management processes which we recommend that they will be called the “pyramid sides” and include: results management, human resources management and general resources management. The three groups are bounded by the “core of management” which we recommend that will be called the “pyramid base”. The pyramid base is connected to each and every phase of the life cycle of the organization, to each process and each result. It includes the school targets and aims which all the school team has to agree upon and there must be an un-doubtful consensus about them.