In this paper, we address one of the main puzzles in finance observed in the stock market by proponents of behavioral finance: the stock predictability puzzle. We offer a statistical model within the context of rational finance which can be used without relying on behavioral finance assumptions to model the predictability of stock returns. We incorporate the predictability of stock returns into the well-known Black-Scholes option pricing formula. Empirically, we analyze the option and spot trader's market predictability of stock prices by defining a forward-looking measure which we call "implied excess predictability". The empirical results indicate the effect of option trader's predictability of stock returns on the price of stock options is an increasing function of moneyness, while this effect is decreasing for spot traders. These empirical results indicate potential asymmetric predictability of stock prices by spot and option traders. We show in pricing options with the strike price significantly higher or lower than the stock price, the predictability of the underlying stock's return should be incorporated into the option pricing formula. In pricing options that have moneyness close to one, stock return predictability is not incorporated into the option pricing model because stock return predictability is the same for both types of traders. In other words, spot traders and option traders are equally informed about the future value of the stock market in this case. Comparing different volatility measures, we find that the difference between implied and realized variances or variance risk premium can potentially be used as a stock return predictor.

Indices of acceptability are well suited to frame the axiomatic features of many performance measures, associated to terminal random cash flows.We extend this notion to classes of c\`adl\`ag processes modelling cash flows over a fixed investment horizon.We provide a representation result for bounded paths. We suggest an acceptability index based both on the static Average Value-at-Risk functional and the running minimum of the paths, which eventually represents a RAROC-type model. Some numerical comparisons clarify the magnitude of performance evaluation for processes.

The complex networks approach has been gaining popularity in analysing investor behaviour and stock markets, but within this approach, initial public offerings (IPO) have barely been explored. We fill this gap in the literature by analysing investor clusters in the first two years after the IPO filing in the Helsinki Stock Exchange by using a statistically validated network method to infer investor links based on the co-occurrences of investors' trade timing for 69 IPO stocks. Our findings show that a rather large part of statistically similar network structures form in different securities and persist in time for mature and IPO companies. We also find evidence of institutional herding.

In a collectivised pension fund, investors agree that any money remaining in the fund when they die can be shared among the survivors.

We give a numerical algorithm to compute the optimal investment-consumption strategy for an infinite collective of identical investors with exponential Kihlstrom--Mirman preferences, investing in the Black--Scholes market in continuous time but consuming in discrete time. Our algorithm can also be applied to an individual investor.

We derive an analytic formula for the optimal consumption in the special case of an individual who chooses not to invest in the financial markets. We prove that our problem formulation for a fund with an infinite number of members is a good approximation to a fund with a large, but finite number of members.

Training a practical and effective model for stock selection has been a greatly concerned problem in the field of artificial intelligence. Even though some of the models from previous works have achieved good performance in the U.S. market by using low-frequency data and features, training a suitable model with high-frequency stock data is still a problem worth exploring. Based on the high-frequency price data of the past several days, we construct two separate models-Convolution Neural Network and Long Short-Term Memory-which can predict the expected return rate of stocks on the current day, and select the stocks with the highest expected yield at the opening to maximize the total return. In our CNN model, we propose improvements on the CNNpred model presented by E. Hoseinzade and S. Haratizadeh in their paper which deals with low-frequency features. Such improvements enable our CNN model to exploit the convolution layer's ability to extract high-level factors and avoid excessive loss of original information at the same time. Our LSTM model utilizes Recurrent Neural Network'advantages in handling time series data. Despite considerable transaction fees due to the daily changes of our stock position, annualized net rate of return is 62.27% for our CNN model, and 50.31% for our LSTM model.

Distributed securities exchanges may become de facto fragmented if they span geographical regions with asymmetric computer infrastructure. First, we build an economic model of a decentralized exchange with two miner clusters, standing in for compact areas of economic activity (e.g., cities). "Local" miners in the area with relatively higher trading activity only join a decentralized exchange if they enjoy a large speed advantage over "long-distance" competitors. This is due to a transfer of economic value across miners, specifically from high- to low-activity clusters. Second, we estimate the speed advantage of "local" over "long-distance" miners in a series of Monte Carlo experiments over a two-cluster, unstructured peer-to-peer network simulated in C. We find that the speed advantage increases in the level of infrastructure asymmetry between clusters. Cross-region DEX blockchains are feasible as long as the asymmetry levels in trading activity and infrastructure availability across regions are positively correlated.

While we would like to predict exact values, available incomplete information is rarely sufficient - usually allowing only to predict conditional probability distributions. This article discusses hierarchical correlation reconstruction (HCR) methodology for such prediction on example of usually unavailable bid-ask spreads, predicted from more accessible data like closing price, volume, high/low price, returns. In HCR methodology we first normalize marginal distributions to nearly uniform like in copula theory. Then we model (joint) densities as linear combinations of orthonormal polynomials, getting its decomposition into (mixed) moments. Then here we model each moment (separately) of predicted variable as a linear combination of mixed moments of known variables using least squares linear regression - getting accurate description with interpretable coefficients describing linear relations between moments. Combining such predicted moments we get predicted density as a polynomial, for which we can e.g. calculate expected value, but also variance to evaluate uncertainty of such prediction, or we can use the entire distribution e.g. for more accurate further calculations or generating random values. There were performed 10-fold cross-validation log-likelihood tests for 22 DAX companies, leading to very accurate predictions, especially when using individual models for each company as there were found large differences between their behaviors. Additional advantage of the discussed methodology is being computationally inexpensive, finding and evaluation a model with hundreds of parameters and thousands of data points takes a second on a laptop.

We introduce a reinforcement learning framework for retail robo-advising. The robo-advisor does not know the investor's risk preference, but learns it over time by observing her portfolio choices in different market environments. We develop an exploration-exploitation algorithm which trades off costly solicitations of portfolio choices by the investor with autonomous trading decisions based on stale estimates of investor's risk aversion. We show that the algorithm's value function converges to the optimal value function of an omniscient robo-advisor over a number of periods that is polynomial in the state and action space. By correcting for the investor's mistakes, the robo-advisor may outperform a stand-alone investor, regardless of the investor's opportunity cost for making portfolio decisions.

Individual level and exhaustive income data for Romania (Cluj county) is analysed for several consecutive years. The income distributions collapse on a master-curve when a properly normalised income is considered. The Beta Prime distribution is appropriate to fit the collapsed data. A dynamical model based on a master equation with growth and reset terms is successful in explaining the observed distribution in a self-consistent manner, i.e. the growth and reset rates are evaluated from the same individual level data. Income distribution derived for other countries are following similar trends. The collapse on the master-curve is not perfect however, suggesting that for a more realistic modelling specific socio-economic characteristics have to be taken also into account.

We present an expansion for portfolio optimization in the presence of small, instantaneous, quadratic transaction costs. Specifically, the magnitude of transaction costs has a coefficient that is of the order $\epsilon$ small, which leads to the optimization problem having an asymptotically-singular Hamilton-Jacobi-Bellman equation whose solution can be expanded in powers of $\sqrt\epsilon$. In this paper we derive explicit formulae for the first two terms of this expansion. Analysis and simulation are provided to show the behavior of this approximating solution.

We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time alignment nor data imputation. Under conditions, this spectral approach is consistent and we provide limit distributions using irregular and asynchronous observations. When observations are synchronous, the Fourier transform method for volatility functionals attains both the optimal convergence rate and the efficient bound in the sense of Le Cam and H\'ajek. Another finding is asynchronicity or missing data as a form of noise produces "interference" in the spectrum estimation and impacts on the convergence rate of volatility functional estimators. This new methodology extends previous applications of volatility functionals, including principal component analysis, generalized method of moments, continuous-time linear regression models et cetera, to high-frequency datasets of which asynchronicity is a prevailing feature.