Existing work on risk-sensitive reinforcement learning - both for symmetric and downside risk measures - has typically used direct Monte-Carlo estimation of policy gradients. While this approach yields unbiased gradient estimates, it also suffers from high variance and decreased sample efficiency compared to temporal-difference methods. In this paper, we study prediction and control with aversion to downside risk which we gauge by the lower partial moment of the return. We introduce a new Bellman equation that upper bounds the lower partial moment, circumventing its non-linearity. We prove that this proxy for the lower partial moment is a contraction, and provide intuition into the stability of the algorithm by variance decomposition. This allows sample-efficient, on-line estimation of partial moments. For risk-sensitive control, we instantiate Reward Constrained Policy Optimization, a recent actor-critic method for finding constrained policies, with our proxy for the lower partial moment. We extend the method to use natural policy gradients and demonstrate the effectiveness of our approach on three benchmark problems for risk-sensitive reinforcement learning.

We consider computation of market values of bonus payments in multi-state with-profit life insurance. The bonus scheme consists of additional benefits bought according to a dividend strategy that depends on the past realization of financial risk, the current individual insurance risk, the number of additional benefits currently held, and so-called portfolio-wide means describing the shape of the insurance business. We formulate numerical procedures that efficiently combine simulation of financial risk with more analytical methods for the outstanding insurance risk. Special attention is given to the case where the number of additional benefits bought only depends on the financial risk.

We provide closed-form pricing formulas for a wide variety of path-independent options, in the exponential L\'evy model driven by the Normal inverse Gaussian process. The results are obtained in both the symmetric and asymmetric model, and take the form of simple and quickly convergent series, under some condition involving the log-forward moneyness and the maturity of instruments. Proofs are based on a factorized representation in the Mellin space for the price of an arbitrary path-independent payoff, and on tools from complex analysis. The validity of the results is assessed thanks to several comparisons with standard numerical methods (Fourier-related inversion, Monte-Carlo simulations) for realistic sets of parameters. Precise bounds for the convergence speed and the truncation error are also provided.

We define the concept of good trade execution and we construct explicit adapted good trade execution strategies in the framework of linear temporary market impact. Good trade execution strategies are dynamic, in the sense that they react to the actual realisation of the traded asset price path over the trading period; this is paramount in volatile regimes, where price trajectories can considerably deviate from their expected value. Remarkably however, the implementation of our strategies does not require the full specification of an SDE evolution for the traded asset price, making them robust across different models. Moreover, rather than minimising the expected trading cost, good trade execution strategies minimise trading costs in a pathwise sense, a point of view not yet considered in the literature. The mathematical apparatus for such a pathwise minimisation hinges on certain random Young differential equations that correspond to the Euler-Lagrange equations of the classical Calculus of Variations. These Young differential equations characterise our good trade execution strategies in terms of an initial value problem that allows for easy implementations.

We investigate the dynamics in the networks of Japanese corporates and its interplay with the appointment of female board members. We find that firms with female board members show homophily with respect to gender and often have above average profitability. We also find that new appointments of women are more likely at boards which observe female board members at other firms to which they are tied by either ownership relations or corporate board interlocks.

We describe the pricing and hedging of financial options without the use of probability using rough paths. By encoding the volatility of assets in an enhancement of the price trajectory, we give a pathwise presentation of the replication of European options. The continuity properties of rough-paths allow us to generalise the so-called fundamental theorem of derivative trading, showing that a small misspecification of the model will yield only a small excess profit or loss of the replication strategy. Our hedging strategy is an enhanced version of classical delta hedging where we use volatility swaps to hedge the second order terms arising in rough-path integrals, resulting in improved robustness.

We show that adversarial reinforcement learning (ARL) can be used to produce market marking agents that are robust to adversarial and adaptively-chosen market conditions. To apply ARL, we turn the well-studied single-agent model of Avellaneda and Stoikov [2008] into a discrete-time zero-sum game between a market maker and adversary. The adversary acts as a proxy for other market participants that would like to profit at the market maker's expense. We empirically compare two conventional single-agent RL agents with ARL, and show that our ARL approach leads to: 1) the emergence of risk-averse behaviour without constraints or domain-specific penalties; 2) significant improvements in performance across a set of standard metrics, evaluated with or without an adversary in the test environment, and; 3) improved robustness to model uncertainty. We empirically demonstrate that our ARL method consistently converges, and we prove for several special cases that the profiles that we converge to correspond to Nash equilibria in a simplified single-stage game.

Mathematical modelling is ubiquitous in the financial industry and drives key decision processes. Any given model provides only a crude approximation to reality and the risk of using an inadequate model is hard to detect and quantify. By contrast, modern data science techniques are opening the door to more robust and data-driven model selection mechanisms. However, most machine learning models are "black-boxes" as individual parameters do not have meaningful interpretation. The aim of this paper is to combine the above approaches achieving the best of both worlds. Combining neural networks with risk models based on classical stochastic differential equations (SDEs), we find robust bounds for prices of derivatives and the corresponding hedging strategies while incorporating relevant market data. The resulting model called neural SDE is an instantiation of generative models and is closely linked with the theory of causal optimal transport. Neural SDEs allow consistent calibration under both the risk-neutral and the real-world measures. Thus the model can be used to simulate market scenarios needed for assessing risk profiles and hedging strategies. We develop and analyse novel algorithms needed for efficient use of neural SDEs. We validate our approach with numerical experiments using both local and stochastic volatility models.

We lightly modify Eriksson's (1996) model to accommodate the home office in a simple model of endogenous growth. By home office we mean any working activity carried out away from the workplace which is assumed to be fixed. Due to the strong mobility restrictions imposed on citizens during the COVID-19 pandemic, we allow the home office to be located at home. At the home office, however, in consequence of the fear and anxiety workers feel because of COVID-19, they become distracted and spend less time working. We show that in the long run, the intertemporal elasticity of substitution of the home-office labor is sufficiently small only if the intertemporal elasticity of substitution of the time spent on distracting activities is small enough also.

On a periodic basis, publicly traded companies report fundamentals, financial data including revenue, earnings, debt, among others. Quantitative finance research has identified several factors, functions of the reported data that historically correlate with stock market performance. In this paper, we first show through simulation that if we could select stocks via factors calculated on future fundamentals (via oracle), that our portfolios would far outperform standard factor models. Motivated by this insight, we train deep nets to forecast future fundamentals from a trailing 5-year history. We propose lookahead factor models which plug these predicted future fundamentals into traditional factors. Finally, we incorporate uncertainty estimates from both neural heteroscedastic regression and a dropout-based heuristic, improving performance by adjusting our portfolios to avert risk. In retrospective analysis, we leverage an industry-grade portfolio simulator (backtester) to show simultaneous improvement in annualized return and Sharpe ratio. Specifically, the simulated annualized return for the uncertainty-aware model is 17.7% (vs 14.0% for a standard factor model) and the Sharpe ratio is 0.84 (vs 0.52).