Classical portfolio optimization often requires forecasting asset returns and their corresponding variances in spite of the low signal-to-noise ratio provided in the financial markets. Deep reinforcement learning (DRL) offers a framework for optimizing sequential trader decisions through an objective which represents its reward function penalized by risk and transaction costs. We investigate the performance of model-free DRL traders in a market environment with frictions and different mean-reverting factors driving the dynamics of the returns. Since this framework admits an exact dynamic programming solution, we can assess limits and capabilities of different value-based algorithms to retrieve meaningful trading signals in a data-driven manner and to reach the benchmark performance. Moreover, extensive simulations show that this approach guarantees flexibility, outperforming the benchmark when the price dynamics is misspecified and some original assumptions on the market environment are violated with the presence of extreme events and volatility clustering.

In this paper, I reply to the recent article by Jeffery and Verheijen (2020) 'A new soil health policy paradigm: Pay for practice not performance!'. While expressing support for their call for a more pronounced role of soil protection in agri-environmental policy, I critically discuss the two main elements of their specific proposal: its emphasis of the concept of soil health and the recommendation to use action-based payments as the main policy instrument. I argue for using soil functions as a more established concept (and thus more adequate for policy purposes), which is also informationally richer than soil health. Furthermore, I provide a more differentiated discussion of the relative advantages and disadvantages of result-based and action-based payments, while addressing the specific criticisms towards the former that Jeffery and Verheijen voice. Also, I suggest an alternative approach (a hybrid model-based scheme) that addresses the limitations of both Jeffery and Verheijen's own proposal and the valid criticisms they direct at result-based payments.

Drivers on the Lyft rideshare platform do not always know where the areas of supply shortage are in real time. This lack of information hurts both riders trying to find a ride and drivers trying to determine how to maximize their earnings opportunity. Lyft's Personal Power Zone (PPZ) product helps the company to maintain high levels of service on the platform by influencing the spatial distribution of drivers in real time via monetary incentives that encourage them to reposition their vehicles. The underlying system that powers the product has two main components: (1) a novel 'escrow mechanism' that tracks available incentive budgets tied to locations within a city in real time, and (2) an algorithm that solves the stochastic driver positioning problem to maximize short-run revenue from riders' fares. The optimization problem is a multiagent dynamic program that is too complicated to solve optimally for our large-scale application. Our approach is to decompose it into two subproblems. The first determines the set of drivers to incentivize and where to incentivize them to position themselves. The second determines how to fund each incentive using the escrow budget. By formulating it as two convex programs, we are able to use commercial solvers that find the optimal solution in a matter of seconds. Rolled out to all 320 cities in which Lyft's operates in a little over a year, the system now generates millions of bonuses that incentivize hundreds of thousands of active drivers to optimally position themselves in anticipation of ride requests every week. Together, the PPZ product and its underlying algorithms represent a paradigm shift in how Lyft drivers drive and generate earnings on the platform. Its direct business impact has been a 0.5% increase in incremental bookings, amounting to tens of millions of dollars per year.

The first half of the paper is devoted to description and implementation of statistical tests arguing for the presence of a Brownian component in the inventories and wealth processes of individual traders. We use intra-day data from the Toronto Stock Exchange to provide empirical evidence of this claim. We work with regularly spaced time intervals, as well as with asynchronously observed data. The tests reveal with high significance the presence of a non-zero Brownian motion component. The second half of the paper is concerned with the analysis of trader behaviors throughout the day. We extend the theoretical analysis of an existing optimal execution model to accommodate the presence of It\^o inventory processes, and we compare empirically the optimal behavior of traders in such fitted models, to their actual behavior as inferred from the data.

This paper studies the finite horizon portfolio management by optimally tracking a ratcheting capital benchmark process. It is assumed that the fund manager can dynamically inject capital into the portfolio account such that the total capital dominates a non-decreasing benchmark floor process at each intermediate time. The tracking problem is formulated to minimize the cost of accumulated capital injection. We first transform the original problem with floor constraints into an unconstrained control problem, however, under a running maximum cost. By identifying a controlled state process with reflection, the problem is further shown to be equivalent to an auxiliary problem, which leads to a nonlinear Hamilton-Jacobi-Bellman (HJB) equation with a Neumann boundary condition. By employing the dual transform, the probabilistic representation and some stochastic flow analysis, the existence of the unique classical solution to the HJB equation is established. The verification theorem is carefully proved, which gives the complete characterization of the feedback optimal portfolio. The application to market index tracking is also discussed when the index process is modeled by a geometric Brownian motion.

Decentralized Finance (DeFi), a blockchain powered peer-to-peer financial system, is mushrooming. One year ago the total value locked in DeFi systems was approximately 700m USD, now, as of April 2021, it stands at around 51bn USD. The frenetic evolution of the ecosystem makes it challenging for newcomers to gain an understanding of its basic features. In this Systematization of Knowledge (SoK), we delineate the DeFi ecosystem along its principal axes. First, we provide an overview of the DeFi primitives. Second, we classify DeFi protocols according to the type of operation they provide. We then go on to consider in detail the technical and economic security of DeFi protocols, drawing particular attention to the issues that emerge specifically in the DeFi setting. Finally, we outline the open research challenges in the ecosystem.

Tail risk protection is in the focus of the financial industry and requires solid mathematical and statistical tools, especially when a trading strategy is derived. Recent hype driven by machine learning (ML) mechanisms has raised the necessity to display and understand the functionality of ML tools. In this paper, we present a dynamic tail risk protection strategy that targets a maximum predefined level of risk measured by Value-At-Risk while controlling for participation in bull market regimes. We propose different weak classifiers, parametric and non-parametric, that estimate the exceedance probability of the risk level from which we derive trading signals in order to hedge tail events. We then compare the different approaches both with statistical and trading strategy performance, finally we propose an ensemble classifier that produces a meta tail risk protection strategy improving both generalization and trading performance.

We present a method for computing the likelihood of a mixed hitting-time model that specifies durations as the first time a latent L\'evy process crosses a heterogeneous threshold. This likelihood is not generally known in closed form, but its Laplace transform is. Our approach to its computation relies on numerical methods for inverting Laplace transforms that exploit special properties of the first passage times of L\'evy processes. We use our method to implement a maximum likelihood estimator of the mixed hitting-time model in MATLAB. We illustrate the application of this estimator with an analysis of Kennan's (1985) strike data.