Log-Optimal Portfolios with Memory Effect

ABSTRACT

In portfolio optimization a classical problem is to trade with assets so as to maximize some kind of utility of the investor. In our paper this problem is investigated for assets whose prices depend on their past values in a non-Markovian way. Such models incorporate several features of real price processes better than Markov processes do. Our utility function is the widespread logarithmic utility, the formulation of the model is discrete in time. Despite the problem being a well-known one, there are few results where memory is treated systematically in a parametric model. Our algorithm is optimal and this optimality is guaranteed for a rich class of model specifications. Moreover, the algorithm runs online, i.e., the optimal investment is achieved in a day-by-day manner, using simple numerical integration, without Monte-Carlo simulations. Theoretical results are demonstrated by numerical experiments as well.     

Long memory volatility in Chinese stock markets

In this study, the long memory property in the volatility of Chinese stock markets is examined. For this purpose, we applied two semi-parametric tests (GPH and LW) and the FIGARCH model, to four Chinese market indices: Shanghai A, Shanghai B, Shenzhen A and Shenzhen B. From the results of our analysis, we can conclude that the volatility of Chinese stock markets exhibits long memory features, and that the assumption of non-normality provides better specifications regarding long memory volatility processes.     

Asymmetric volatility, volatility clustering, and herding agents with a borrowing constraint

Recent empirical research has documented asymmetric volatility and volatility clustering in stock markets. We conjecture that a limit of arbitrage due to a borrowing constraint and herding behavior by investors are related to these phenomena. This study conducts simulation analyses on a spin model where borrowing constrained agents imitate their nearest neighbors but switch their strategies to a different one intermittently. We show that herding matters for volatility clustering while a borrowing constraint intensifies the asymmetry of volatility through the herding effect.     

Volatility estimators and the inverse range process in a random volatility random walk and Wiener processes

The purpose of this paper is to study the mean, the variance, the probability distribution and the hazard rate of the inverse range process of an a-priori unknown volatility random walk. Motivation for this process arises when it is necessary to obtain statistics that pertain to a process volatility in addition to the usual variance statistics. As a result, range process statistics are indicated as an additional source of information in the study of processes’ volatility. Examples and applications are considered.     

Long memory and volatility clustering: Is the empirical evidence consistent across stock markets?

Long memory and volatility clustering are two stylized facts frequently related to financial markets. Traditionally, these phenomena have been studied based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and FIGARCH, inter alia. One advantage of these models is their ability to capture nonlinear dynamics. Another interesting manner to study the volatility phenomenon is by using measures based on the concept of entropy. In this paper we investigate the long memory and volatility clustering for the SP 500, NASDAQ 100 and Stoxx 50 indexes in order to compare the US and European Markets. Additionally, we compare the results from conditionally heteroscedastic models with those from the entropy measures. In the latter, we examine Shannon entropy, Renyi entropy and Tsallis entropy. The results corroborate the previous evidence of nonlinear dynamics in the time series considered.     

Denseness of volatile and nonvolatile sequences of functions

In a recent paper by Jonasson and Steif, definitions to describe the volatility of sequences of Boolean functions, $f_n:{\{?1,1\}}^n\to \{?1,1\}$ were introduced. We continue their study of how these definitions relate to noise stability and noise sensitivity. Our main results are that the set of volatile sequences of Boolean functions is a natural way “dense” in the set of all sequences of Boolean functions, and that the set of non-volatile Boolean sequences is not “dense” in the set of noise stable sequences of Boolean functions.     

用光镊技术研究硝酸铵气溶胶的挥发性

研究半挥发性气溶胶物质的气粒分配对于更准确地描述大气气溶胶的组成和尺寸分布是至关重要的。硝酸铵是亚微米颗粒物的主要组成部分,特别是在高污染事件中。为了更深入的了解硝酸铵气溶胶的气粒分配问题,利用激光悬浮技术捕获、悬浮半挥发性无机物硝酸铵液滴单颗粒（2～10 μm）,控制相对湿度条件、温度条件,并采集氢-氧振动带的受激拉曼峰位信息,利用非弹性米氏散射理论计算实时液滴半径尺寸、折射率和浓度,利用稳态传质模型Maxwell公式推算出了不同湿度下的蒸汽压。实验数据计算出的硝酸铵的饱和蒸汽压值的数量级与文献报道一致。当RH分别恒定在80%, 73%, 68%, 57.3%, 55.4%, 44.8%时,饱和蒸汽压值为(1.67±0.24)×10-3, (1.82±0.19)×10-3, (2.91±0.13)×10-3, (3.5±0.28)×10-3, (4.59±0.22)×10-3和(6.64±0.3)×10-3 Pa,显然,随着相对湿度的降低,饱和蒸汽压值增大,即湿度降低促进硝酸铵的挥发。此外,还推算了不同湿度下硝酸铵气溶胶液滴的挥发通量,挥发通量值在(4.01±0.79)×10-7～(3.32±0.77)×10-8 mol·(s·m2)-1之间。这对更好的了解气溶胶在挥发过程中的微观过程有重要意义。     

Synthesis and properties of a new ketoiminate derivative of the 2,2,6,6-tetramethylheptane-3,5-dionate ligand to prepare volatile CVD precursors

The β-ketoimine (CH₃)₃CC(NH₂)CHC(O)C(CH₃)₃ (1) was synthesized by amination with dry ammonia in the presence of TiCl₄. M.p. = 131 °C. IR and ¹H and ¹³C NMR spectroscopic characterization indicates that the structure of a solution of 1 is the ketone form, and a single-crystal X-ray diffraction study shows that the structure of 1 is the enaminoketone form. The reaction of 1 with copper(II) and nickel(II) salts in solution gave chelate metal complexes: Cu[(CH₃)₃CC(NH)CHC(O)C(CH₃)₃]₂ (2), M.p. = 209 °C, and Ni[(CH₃)₃CC(NH)CHC(O)C(CH₃)₃]₂ (3), M.p. = 267 °C. These complexes are volatile and sublime at 180–190 °C at 5 × 10⁻³ Torr. An X-ray diffraction study reveals that these metal complexes are monomeric and isostructural in the solid state. In compound 2, the Cu atom has a square coordination environment: Cu–O ≈ Cu–N = 1.91 Å, ∠O–Cu–N = 91.81 Å.     

Reconstructing local volatility using total variation

The aim of this paper is to identify the volatility function in Dupire’s equation from given option prices. This inverse problem is formulated as an infinite-dimensional minimization problem with PDE constraints. The computational cost of solving the discretized problem on a fine discretization level is expensive. A multi-grid method is proposed to explore the hierarchical structures of discretized problems on different levels. Computational examples are presented to demonstrate the efficiency of our method.     

Levelling the playing field: A VIX-linked structure for funded pension schemes

In this article, we study intergenerational risk and cost sharing for a variety of collective funded pension plans. Inspired by the literature on contingent claim analysis in pension insurance, we derive time-varying contribution and benefit levels. The latter specifically include the fund surplus, which accounts for (intergenerational) risk sharing, and the VIX, which is related to cost sharing among generations. We find that pension schemes with a well-structured volatility-risk-adjusted component can be welfare enhancing for the entry and future cohorts. In addition, these schemes are fair from an ex ante perspective, provide adequate consumption profiles and high levels of satisfaction.