While standard estimation assumes that all datapoints are from probability distribution of the same fixed parameters $\theta$, we will focus on maximum likelihood (ML) adaptive estimation for nonstationary time series: separately estimating parameters $\theta_T$ for each time $T$ based on the earlier values $(x_t)_{t<T}$ using (exponential) moving ML estimator $\theta_T=\arg\max_\theta l_T$ for $l_T=\sum_{t<T} \eta^{T-t} \ln(\rho_\theta (x_t))$ and some $\eta\in(0,1]$. Computational cost of such moving estimator is generally much higher as we need to optimize log-likelihood multiple times, however, in many cases it can be made inexpensive thanks to dependencies. We focus on such example: $\rho(x)\propto \exp(-|(x-\mu)/\sigma|^\kappa/\kappa)$ exponential power distribution (EPD) family, which covers wide range of tail behavior like Gaussian ($\kappa=2$) or Laplace ($\kappa=1$) distribution. It is also convenient for such adaptive estimation of scale parameter $\sigma$ as its standard ML estimation is $\sigma^\kappa$ being average $\|x-\mu\|^\kappa$. By just replacing average with exponential moving average: $(\sigma_{T+1})^\kappa=\eta(\sigma_T)^\kappa +(1-\eta)|x_T-\mu|^\kappa$ we can inexpensively make it adaptive. It is tested on daily log-return series for DJIA companies, leading to essentially better log-likelihoods than standard (static) estimation, with optimal $\kappa$ tails types varying between companies. Presented general alternative estimation philosophy provides tools which might be useful for building better models for analysis of nonstationary time-series.

In financial automatic feature construction task, genetic programming (GP) is the state-of-the-art technique. It employs reverse polish expression to represent features and then simulate the evolution process. However, with the development of deep learning, more choices to design this algorithm are available. This paper proposes Alpha Discovery Neural Network (ADNN), equipped with different kinds of feature extractors to construct diversified financial technical factors based on prior knowledge. The experiment result shows that both fully-connected network and recurrent network are good at extracting information from financial time series, but convolution network structure can not effectively extract this information. ADNN effectively enrich the current factor pool because in all cases, ADNN can construct more informative and diversified features than GP. Moreover, features constructed by ADNN can always improve original strategy return, Sharpe ratio and max draw-down.

This paper investigates a financial market where stock returns depend on a hidden Gaussian mean reverting drift process. Information on the drift is obtained from returns and expert opinions in the form of noisy signals about the current state of the drift arriving at the jump times of a homogeneous Poisson process. Drift estimates are based on Kalman filter techniques and described by the conditional mean and covariance matrix of the drift given the observations. We study the filter asymptotics for increasing arrival intensity of expert opinions and prove that the conditional mean is a consistent drift estimator, it converges in the mean-square sense to the hidden drift. Thus, in the limit as the arrival intensity goes to infinity investors have full information about the drift.

Given the importance of public support for policy change and implementation, public policymakers and researchers have attempted to understand the factors associated with this support for climate change mitigation policy. In this article, we compare the feasibility of using different supervised learning methods for regression using a novel socio-economic data set which measures public support for potential climate change mitigation policies. Following this model selection, we utilize gradient boosting regression, a well-known technique in the machine learning community, but relatively uncommon in public policy and public opinion research, and seek to understand what factors among the several examined in previous studies are most central to shaping public support for mitigation policies in climate change studies. The use of this method provides novel insights into the most important factors for public support for climate change mitigation policies. Using national survey data, we find that the perceived risks associated with climate change are more decisive for shaping public support for policy options promoting renewable energy and regulating pollutants. However, we observe a very different behavior related to public support for increasing the use of nuclear energy where climate change risk perception is no longer the sole decisive feature. Our findings indicate that public support for renewable energy is inherently different from that for nuclear energy reliance with the risk perception of climate change, dominant for the former, playing a subdued role for the latter.

On January 3, 2018 MiFID II regulations came into effect. This paper compares properties of European stocks for 2017 and 2018. The introduced tick size regime impacted the microstructure in accordance with existing literature on tick size changes. Remarkably, the modification of the microstructure also impacted volatility and transacted volume. Furthermore, it is shown that closing auction volumes increased heavily since MiFID II, leading to higher absolute returns in the auctions. Before MiFID II, high closing auction returns reverted overnight, but after MiFID II this reversion disappeared, showing that closing prices became more efficient.

What is the best market-neutral implementation of classical Equity Factors? Should one use the specific predictability of the short-leg to build a zero beta Long-Short portfolio, in spite of the specific costs associated to shorting, or is it preferable to ban the shorts and hedge the long-leg with -- say -- an index future? We revisit this question by focusing on the relative predictability of the two legs, the issue of diversification, and various sources of costs. Our conclusion is that, using the same Factors, a Long-Short implementation leads to superior risk-adjusted returns than its Hedged Long-Only counterpart, at least when Assets Under Management are not too large.

Automated market makers, first popularized by Hanson's Logarithmic Market Scoring Rule for prediction markets, have become important building blocks (often called 'primitives') for decentralized finance. A particularly useful primitive is the ability to measure the price of an asset, a problem often known as the pricing oracle problem. In this paper, we focus on the analysis of a very large class of automated market makers, called constant function market makers, which includes popular market makers such as Uniswap and Balancer. We give sufficient conditions such that, under fairly general assumptions, agents who interact with these constant function market makers are incentivized to correctly report the price of an asset. We also derive several other useful properties including liquidity provider returns in the path independent case.

We consider the problem of seeking an optimal set of model points associated to a fixed portfolio of life insurance policies. Such an optimal set is characterized by minimizing a certain risk functional, which gauges the average discrepancy with the fixed portfolio in terms of the fluctuation of the interest rate term structure within a given time horizon. We prove a representation theorem which provides two alternative formulations of the risk functional and which may be understood in connection with the standard approaches for the portfolio immunization based on sensitivity analysis. For this purpose, a general framework concerning some techniques of stochastic integration in Banach space and Malliavin calculus is introduced. A numerical example is discussed when considering a portfolio of whole life policies.

We study the ex-ante maximization of market efficiency, defined in terms of minimum deviation of market prices from fundamental values, from a centralized planner's perspective. Prices are pressured from exogenous trading actions of leverage targeting banks, which rebalance their portfolios in response to asset shocks. We develop an explicit expression for the matrix of asset holdings which minimizes market inefficiency, and characterize it in terms of two key sufficient statistics: the banks' systemic significances and the statistical moments of asset shocks. Our analysis shows that higher homogeneity in banks' systemic significances requires banks' portfolio holdings to be further away from a full diversification strategy to reduce inefficiencies.

I study endogenous learning dynamics for people expecting systematic reversals from random sequences - the "gambler's fallacy." Biased agents face an optimal-stopping problem. They are uncertain about the underlying distribution and learn its parameters from predecessors. Agents stop when early draws are "good enough," so predecessors' experience contain negative streaks but not positive streaks. Since biased agents understate the likelihood of consecutive below-average draws, society converges to over-pessimistic beliefs about the distribution's mean and stops too early. Agents uncertain about the distribution's variance overestimate it to an extent that depends on predecessors' stopping thresholds. Subsidizing search partially mitigates long-run belief distortions.

This paper investigates optimal consumption, investment, and healthcare spending under Epstein-Zin preferences. Given consumption and healthcare spending plans, Epstein-Zin utilities are defined over an agent's random lifetime, partially controllable by the agent as healthcare reduces Gompertz' natural growth rate of mortality. In a Black-Scholes market, the stochastic optimization problem is solved through the associated Hamilton-Jacobi-Bellman (HJB) equation. Compared with classical Epstein-Zin utility maximization, the additional controlled mortality process complicates the uniqueness of Epstein-Zin utilities and verification arguments. A combination of probabilistic arguments and analysis of the HJB equation are required to resolve the challenges. In contrast to prior work under time-separable utilities, Epstein-Zin preferences largely facilitate calibration. In four different countries we examined, the model-generated mortality closely approximates actual mortality data; moreover, the calibrated efficacy of healthcare is in broad agreement with empirical studies on healthcare across countries.

In this paper the zero vanna implied volatility approximation for the price of freshly minted volatility swaps is generalised to seasoned volatility swaps. We also derive how volatility swaps can be hedged using a strip of vanilla options with weights that are directly related to trading intuition. Additionally, we derive first and second order hedges for volatility swaps using only variance swaps. As dynamically trading variance swaps is in general cheaper and operationally less cumbersome compared to dynamically rebalancing a continuous strip of options, our result makes the hedging of volatility swaps both practically feasible and robust. Within the class of stochastic volatility models our pricing and hedging results are model-independent and can be implemented at almost no computational cost.

This letter expands the studies of the informational efficiency in the cryptocurrency market. Most studies have focused on Bitcoin, the foremost known cryptocurrency, and a few more coins. However, this market is more diverse, with cryptocurrencies entering and leaving the market on a weekly basis. This letter fills an important gap in the literature, by studying the informational efficiency using a multi-scaling methodology, which represents a new approach. We compute the generalized Hurst exponent of eighty-four cryptoassets daily returns. The multi-scaling methodology used in this paper find compelling evidence that cryptocurrencies have different degree of long range dependence, and --more importantly -- follow different stochastic processes. Some of them follow traditional monofractal models consistent with fractional Brownian motion, while others exhibit complex multifractal dynamics.

Motivation for this paper is to understand the impact of information on asset price bubbles and perceived arbitrage opportunities. This boils down to study optional projections of $\mathbb{G}$-adapted strict local martingales into a smaller filtration $\mathbb{F}$ under equivalent martingale measures. We give some general results as well as analyze in details two specific examples given by the inverse three dimensional Bessel process and a class of stochastic volatility models.

We present a parsimonious stochastic model for valuation of options on the fraction of infected individuals during an epidemic. The underlying stochastic dynamical system is a stochastic differential version of the SIR model of mathematical epidemiology.

In this paper, we study the financial and economic implications of a zombie epidemic on a major industrialized nation. We begin with a consideration of the epidemiological modeling of the zombie contagion. The emphasis of this work is on the computation of direct and indirect financial consequences of this contagion of the walking dead. A moderate zombie outbreak leaving 1 million people dead in a major industrialized nation could result in GDP losses of 23.44% over the subsequent year and a drop in financial market of 29.30%. We conclude by recommending policy actions necessary to prevent this potential economic collapse.

Reinforcement learning algorithms describe how an agent can learn an optimal action policy in a sequential decision process, through repeated experience. In a given environment, the agent policy provides him some running and terminal rewards. As in online learning, the agent learns sequentially. As in multi-armed bandit problems, when an agent picks an action, he can not infer ex-post the rewards induced by other action choices. In reinforcement learning, his actions have consequences: they influence not only rewards, but also future states of the world. The goal of reinforcement learning is to find an optimal policy -- a mapping from the states of the world to the set of actions, in order to maximize cumulative reward, which is a long term strategy. Exploring might be sub-optimal on a short-term horizon but could lead to optimal long-term ones. Many problems of optimal control, popular in economics for more than forty years, can be expressed in the reinforcement learning framework, and recent advances in computational science, provided in particular by deep learning algorithms, can be used by economists in order to solve complex behavioral problems. In this article, we propose a state-of-the-art of reinforcement learning techniques, and present applications in economics, game theory, operation research and finance.

This survey develops a dual analysis, consisting, first, in a bibliometric examination and, second, in a close literature review of all the scientific production around cryptocurrencies conducted in economics so far. The aim of this paper is twofold. On the one hand, proposes a methodological hybrid approach to perform comprehensive literature reviews. On the other hand, we provide an updated state of the art in cryptocurrency economic literature. Our methodology emerges as relevant when the topic comprises a large number of papers, that make unrealistic to perform a detailed reading of all the papers. This dual perspective offers a full landscape of cryptocurrency economic research. Firstly, by means of the distant reading provided by machine learning bibliometric techniques, we are able to identify main topics, journals, key authors, and other macro aggregates. Secondly, based on the information provided by the previous stage, the traditional literature review provides a closer look at methodologies, data sources and other details of the papers. In this way, we offer a classification and analysis of the mounting research produced in a relative short time span.