The Lightning Network is a so-called second-layer technology built on top of the Bitcoin blockchain to provide "off-chain" fast payment channels between users, which means that not all transactions are settled and stored on the main blockchain. In this paper, we model the emergence of the Lightning Network as a (bond) percolation process and we explore how the distributional properties of the volume and size of transactions per user may impact its feasibility. The agents are all able to reciprocally transfer Bitcoins using the main blockchain and also - if economically convenient - to open a channel on the Lightning Network and transact "off chain". We base our approach on fitness-dependent network models: as in real life, a Lightning channel is opened with a probability that depends on the "fitness" of the concurring nodes, which in turn depends on wealth and volume of transactions. The emergence of a connected component is studied numerically and analytically as a function of the parameters, and the phase transition separating regions in the phase space where the Lightning Network is sustainable or not is elucidated. We characterize the phase diagram determining the minimal volume of transactions that would make the Lightning Network sustainable for a given level of fees or, alternatively, the maximal cost the Lightning ecosystem may impose for a given average volume of transactions. The model includes parameters that could be in principle estimated from publicly available data once the evolution of the Lighting Network will have reached a stationary operable state, and is fairly robust against different choices of the distributions of parameters and fitness kernels.

Inverse reinforcement learning has proved its ability to explain state-action trajectories of expert agents by recovering their underlying reward functions in increasingly challenging environments. Recent advances in adversarial learning have allowed extending inverse RL to applications with non-stationary environment dynamics unknown to the agents, arbitrary structures of reward functions and improved handling of the ambiguities inherent to the ill-posed nature of inverse RL. This is particularly relevant in real time applications on stochastic environments involving risk, like volatile financial markets. Moreover, recent work on simulation of complex environments enable learning algorithms to engage with real market data through simulations of its latent space representations, avoiding a costly exploration of the original environment. In this paper, we explore whether adversarial inverse RL algorithms can be adapted and trained within such latent space simulations from real market data, while maintaining their ability to recover agent rewards robust to variations in the underlying dynamics, and transfer them to new regimes of the original environment.

Detecting structure in noisy time series is a difficult task. One intuitive feature is the notion of trend. From theoretical hints and using simulated time series, we empirically investigate the efficiency of standard recurrent neural networks (RNNs) to detect trends. We show the overall superiority and versatility of certain standard RNNs structures over various other estimators. These RNNs could be used as basic blocks to build more complex time series trend estimators.

We apply the procedure of Lee et al. to the problem of performing inference on the signal-noise ratio of the asset which displays maximum sample Sharpe ratio over a set of possibly correlated assets. We find a multivariate analogue of the commonly used approximate standard error of the Sharpe ratio to use in this conditional estimation procedure. We also consider several alternative procedures, including the simple Bonferroni correction for multiple hypothesis testing, which we fix for the case of positive common correlation among assets, the chi-bar square test against one-sided alternatives, Follman's test, and Hansen's asymptotic adjustments.

Testing indicates the conditional inference procedure achieves nominal type I rate, and does not appear to suffer from non-normality of returns. The conditional estimation test has low power under the alternative where there is little spread in the signal-noise ratios of the assets, and high power under the alternative where a single asset has high signal-noise ratio. Unlike the alternative procedures, it appears to enjoy rejection probabilities montonic in the signal-noise ratio of the selected asset.

This paper investigates the large-time asymptotic behavior of the sensitivities of cash flows. In quantitative finance, the price of a cash flow is expressed in terms of a pricing operator of a Markov diffusion process. We study the extent to which the pricing operator is affected by small changes of the underlying Markov diffusion. The main idea is a partial differential equation (PDE) representation of the pricing operator by incorporating the Hansen--Scheinkman decomposition method. The sensitivities of the cash flows and their large-time convergence rates can be represented via simple expressions in terms of eigenvalues and eigenfunctions of the pricing operator. Furthermore, compared to the work of Park (Finance Stoch. 4:773-825, 2018), more detailed convergence rates are provided. In addition, we discuss the application of our results to three practical problems: utility maximization, entropic risk measures, and bond prices. Finally, as examples, explicit results for several market models such as the Cox--Ingersoll--Ross (CIR) model, 3/2 model and constant elasticity of variance (CEV) model are presented.

We design and implement a novel experimental test of subjective expected utility theory and its generalizations. Our experiments are implemented in the laboratory with a student population and pushed out through a large-scale panel to a general sample of the U.S.\ population. We find that a majority of subjects' choices are consistent with the maximization of {\em some} utility function, but not with subjective utility theory. The theory is tested by gauging how subjects respond to price changes. A majority of subjects respond to price changes in the direction predicted by the theory, but not to a degree that makes them fully consistent with subjective expected utility. Surprisingly, maxmin expected utility adds no explanatory power to subjective expected utility.

Our findings remain the same regardless of whether we look at laboratory data or the panel survey, even though the two subject populations are very different. The degree of violations of subjective expected utility theory is not affected by age nor cognitive ability, but it is correlated with financial literacy.

The paper introduces a simple way of recording and manipulating stochastic processes without explicit reference to a probability measure. In the new calculus, operations traditionally presented in a measure-specific way are instead captured by tracing the behaviour of jumps (also when no jumps are physically present). The new calculus is thus intuitive and compact. The calculus is also fail-safe in that, under minimal assumptions, all formal calculations are guaranteed to yield mathematically well-defined stochastic processes. Several illustrative examples of the new concept are given, among them a novel result on the Margrabe option to exchange one defaultable asset for another.

Using purely probabilistic argument, we prove the global well-posedness of multidimensional superquadratic backward stochastic differential equations (BSDEs) without Markovian assumption. The key technique is the interplay between the local well-posedness of fully coupled path-dependent forward backward stochastic differential equations and backward iterations of the superquadratic BSDE. The superquadratic BSDE in this article includes quadratic BSDEs appear in stochastic differential game and price impact model. Our result also provides the well-posedness of a system of path-dependent quasilinear PDE that generalizes Ladyzhenskaia and Uraltseva (1968).

The literature on optimal reinsurance does not deal with how much the effectiveness of such solutions is degraded by errors in parameters and models. The issue is investigated through both asymptotics and numerical studies. It is shown that the rate of degradation is often $O(1/n)$ as the sample size $n$ of historical observations becomes infinite. Criteria based on Value at Risk are exceptions that may achieve only $O(1/\sqrt{n})$. These theoretical results are supported by numerical studies. A Bayesian perspective on how to integrate risk caused by parameter error is offered as well.

This study investigates the socio-demographic characteristics that individual cryptocurrency investors exhibit and the factors which go into their investment decisions in different Initial Coin Offerings. A web based revealed preference survey was conducted among Australian and Chinese blockchain and cryptocurrency followers, and a Multinomial Logit model was applied to inferentially analyze the characteristics of cryptocurrency investors and the determinants of the choice of investment in cryptocurrency coins versus other types of ICO tokens. The results show a difference between the determinant of these two choices among Australian and Chinese cryptocurrency folks. The significant factors of these two choices include age, gender, education, occupation, and investment experience, and they align well with the behavioural literature. Furthermore, alongside differences in how they rank the attributes of ICOs, there is further variance between how Chinese and Australian investors rank deterrence factors and investment strategies.

This paper investigates the so-called leakage effect of trading strategies generated functionally from rank-dependent portfolio generating functions. This effect measures the loss in wealth of trading strategies due to renewing the portfolio constituent stocks. Theoretically, the leakage effect of a trading strategy is expressed explicitly by a finite-variation term. The computation of the leakage is different from what previous research has suggested. The method to estimate leakage in discrete time is then introduced with some practical considerations. An empirical example illustrates the leakage of the corresponding trading strategies under different constituent list sizes.

We study the problem of maximising terminal utility for an agent facing model uncertainty, in a frictionless discrete-time market with one safe asset and finitely many risky assets. We show that an optimal investment strategy exists if the utility function, defined either over the positive real line or over the whole real line, is bounded from above. We further find that the boundedness assumption can be dropped provided that we impose suitable integrability conditions, related to some strengthened form of no-arbitrage. These results are obtained in an alternative framework for model uncertainty, where all possible dynamics of the stock prices are represented by a collection of stochastic processes on the same filtered probability space, rather than by a family of probability measures.

Financial market in oil-dependent countries has been always influenced by any changes in international energy market, In particular, oil price.It is therefore of considerable interest to investigate the impact of oil price on financial markets. The aim of this paper is to model the impact of oil price volatility on stock and industry indices by considering gas and gold price,exchange rate and trading volume as explanatory variables. We also propose Feed-forward networks as an accurate method to model non-linearity. we use data from 2009 to 2018 that is split in two periods during international energy sanction and post-sanction. The results show that Feed-forward networks perform well in predicting variables and oil price volatility has a significant impact on stock and industry market indices. The result is more robust in the post-sanction period and global financial crisis in 2014. Herein, it is important for financial market analysts and policy makers to note which factors and when influence the financial market, especially in an oil-dependent country such as Iran with uncertainty in the international politics. This research analyses the results in two different periods, which is important in the terms of oil price shock and international energy sanction. Also, using neural networks in methodology gives more accurate and reliable results. Keywords: Feed-forward networks,Industry index,International energy sanction,Oil price volatility

In this paper we re-analyse the transition from sure to probabilistic sniping as explored in Menkveld and Zoican [14]. In that paper, the authors introduce a stylized version of a competitive game in which high frequency traders (HFTs) interact with each other and liquidity traders. The authors show that risk aversion plays an important role in the transition from sure to mixed (or probabilistic) sniping. In this paper, we re-interpret and extend these conclusions in the context of repeated games and highlight some differences in results. In particular, we identify situations in which probabilistic sniping is genuinely profitable that are qualitatively different from the ones obtained in [14]. Keywords: algorithmic trading,sniping, electronic exchange,high-frequency traders,Nash equilibrium,repeated games,bandits, subgame-perfect equilibrium,transition

We consider a general path-dependent version of the hedging problem with price impact of Bouchard et al. (2019), in which a dual formulation for the super-hedging price is obtained by means of PDE arguments, in a Markovian setting and under strong regularity conditions. Using only probabilistic arguments, we prove, in a path-dependent setting and under weak regularity conditions, that any solution to this dual problem actually allows one to construct explicitly a perfect hedging portfolio. From a pure probabilistic point of view, our approach also allows one to exhibit solutions to a specific class of second order forward backward stochastic differential equations, in the sense of Cheridito et al. (2007). Existence of a solution to the dual optimal control problem is also addressed in particular settings. As a by-product of our arguments, we prove a version of It{\^o}'s Lemma for path-dependent functionals that are only C^{0,1} in the sense of Dupire.

Tax evasion is the illegal non-payment of taxes by individuals, corporations, and trusts. It results in a loss of state revenue that can undermine the effectiveness of government policies. One measure of tax evasion is the so-called tax gap: the difference between the income that should be reported to the tax authorities and the amount actually reported. However, economists lack a robust method for estimating the tax gap through a bottom-up approach based on fiscal audits. This is difficult because the declared tax base is available on the whole population but the income reported to the tax authorities is generally available only on a small, non-random sample of audited units. This induces a selection bias which invalidates standard statistical methods. Here, we use machine learning based on a 2-steps Gradient Boosting model, to correct for the selection bias without requiring any strong assumption on the distribution. We use our method to estimate the Italian VAT Gap related to individual firms based on information gathered from administrative sources. Our algorithm estimates the potential VAT turnover of Italian individual firms for the fiscal year 2011 and suggests that the tax gap is about 30% of the total potential tax base. Comparisons with other methods show our technique offers a significant improvement in predictive performance.