In financial automatic feature construction task, genetic programming is the state-of-the-art-technic. It uses reverse polish expression to represent features and then uses genetic programming to simulate the evolution process. With the development of deep learning, there are more powerful feature extractors for option. And we think that comprehending the relationship between different feature extractors and data shall be the key. In this work, we put prior knowledge into alpha discovery neural network, combined with different kinds of feature extractors to do this task. We find that in the same type of network, simple network structure can produce more informative features than sophisticated network structure, and it costs less training time. However, complex network is good at providing more diversified features. In both experiment and real business environment, 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.

We analyze a market impact game between $n$ risk averse agents who compete for liquidity in a market impact model with permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. Our first main result characterizes the Nash equilibrium in terms of a fully coupled system of forward-backward stochastic differential equations (FBSDEs). Our second main result provides conditions under which this system of FBSDEs has indeed a unique solution, which in turn yields the unique Nash equilibrium. We furthermore obtain closed-form solutions in special situations and analyze them numerically

Proof of Stake (PoS) is a burgeoning Sybil resistance mechanism that aims to have a digital asset ("token") serve as security collateral in crypto networks. However, PoS has so far eluded a comprehensive threat model that encompasses both Byzantine attacks from distributed systems and financial attacks that arise from the dual usage of the token as a means of payment and a Sybil resistance mechanism. In particular, the existence of derivatives markets makes malicious coordination among validators easier to execute than in Proof of Work systems. We demonstrate that it is also possible for on-chain lending smart contracts to cannibalize network security in PoS systems. When the yield provided by these contracts is more attractive than the inflation rate provided from staking, stakers will tend to remove their staked tokens and lend them out, thus reducing network security. In this paper, we provide a simple stochastic model that describes how rational validators with varying risk preferences react to changes in staking and lending returns. For a particular configuration of this model, we provide a formal proof of a phase transition between equilibria in which tokens are predominantly staked and those in which they are predominantly lent. We further validate this emergent adversarial behavior (e.g. reduced staked token supply) with agent-based simulations that sample transitions under more realistic conditions. Our results illustrate that rational, non-adversarial actors can dramatically reduce PoS network security if block rewards are not calibrated appropriately above the expected yields of on-chain lending.

The term structure of interest rates or yield curve is a function relating the interest rate with its own term. Nonlinear regression models of Nelson-Siegel and Svensson were used to estimate the yield curve using a sample of historical data supplied by the National Stock Exchange of Costa Rica. The optimization problem involved in the estimation process of model parameters is addressed by the use of four well known combinatorial optimization metaheuristics: Ant colony optimization, Genetic algorithm, Particle swarm optimization and Simulated annealing. The aim of the study is to improve the local minima obtained by a classical quasi-Newton optimization method using a descent direction. Good results with at least two metaheuristics are achieved, Particle swarm optimization and Simulated annealing. Keywords: Yield curve, nonlinear regression, Nelson-

Unfair stock trading strategies have been shown to be one of the most negative perceptions that customers can have concerning trading and may result in long-term losses for a company. Investment banks usually place trading orders for multiple clients with the same target assets but different order sizes and diverse requirements such as time frame and risk aversion level, thereby total earning and individual earning cannot be optimized at the same time. Orders executed earlier would affect the market price level, so late execution usually means additional implementation cost. In this paper, we propose a novel scheme that utilizes multi-agent reinforcement learning systems to derive stock trading strategies for all clients which keep a balance between revenue and fairness. First, we demonstrate that Reinforcement learning (RL) is able to learn from experience and adapt the trading strategies to the complex market environment. Secondly, we show that the Multi-agent RL system allows developing trading strategies for all clients individually, thus optimizing individual revenue. Thirdly, we use the Generalized Gini Index (GGI) aggregation function to control the fairness level of the revenue across all clients. Lastly, we empirically demonstrate the superiority of the novel scheme in improving fairness meanwhile maintaining optimization of revenue.

Multiple studies have documented racial, gender, political ideology, or ethnical biases in comparative judicial systems. Supplementing this literature, we investigate whether judges rule cases differently when one of the litigants is a politician. We suggest a theory of power collusion, according to which judges might use rulings to buy cooperation or threaten members of the other branches of government. We test this theory using a sample of small claims cases in the state of S\~ao Paulo, Brazil, where no collusion should exist. The results show a negative bias of 3.7 percentage points against litigant politicians, indicating that judges punish, rather than favor, politicians in court. This punishment in low-salience cases serves as a warning sign for politicians not to cross the judiciary when exercising checks and balances, suggesting yet another barrier to judicial independence in development settings.

In this paper, we combine modern portfolio theory and option pricing theory so that a trader who takes a position in a European option contract and the underlying assets can construct an optimal portfolio such that at the moment of the contract's maturity the contract is perfectly hedged. We derive both the optimal holdings in the underlying assets for the trader's optimal mean-variance portfolio and the amount of unhedged risk prior to maturity. Solutions assuming the cases where the price dynamics in the underlying assets follow discrete binomial price dynamics, continuous diffusions, stochastic volatility, volatility-of-volatility, and Merton-jump diffusion are derived.