We propose a mathematical model of momentum risk-taking, which is essentially real-time risk management focused on short-term volatility of stock markets. Its implementation, our fully automated momentum equity trading system presented systematically, proved to be successful in extensive historical and real-time experiments. Momentum risk-taking is one of the key components of general decision-making, a challenge for artificial intelligence and machine learning with deep roots in cognitive science; its variants beyond stock markets are discussed. We begin with a new algebraic-type theory of news impact on share-prices, which describes well their power growth, periodicity, and the market phenomena like price targets and profit-taking. This theory generally requires Bessel and hypergeometric functions. Its discretization results in some tables of bids, which are basically expected returns for main investment horizons, the key in our trading system. The ML procedures we use are similar to those in neural networking. A preimage of our approach is the new contract card game provided at the end, a combination of bridge and poker. Relations to random processes and the fractional Brownian motion are outlined.

SREC markets are a relatively novel market-based system to incentivize the production of energy from solar means. A regulator imposes a floor on the amount of energy each regulated firm must generate from solar power in a given period and provides them with certificates for each generated MWh. Firms offset these certificates against the floor and pay a penalty for any lacking certificates. Certificates are tradable assets, allowing firms to purchase/sell them freely. In this work, we formulate a stochastic control problem for generating and trading in SREC markets from a regulated firm's perspective. We account for generation and trading costs, the impact both have on SREC prices, provide a characterization of the optimal strategy, and develop a numerical algorithm to solve this control problem. Through numerical experiments, we explore how a firm who acts optimally behaves under various conditions. We find that an optimal firm's generation and trading behaviour can be separated into various regimes, based on the marginal benefit of obtaining an additional SREC, and validate our theoretical characterization of the optimal strategy. We also conduct parameter sensitivity experiments and conduct comparisons of the optimal strategy to other candidate strategies.

Risk measures connect probability theory or statistics to optimization, particularly to convex optimization. They are nowadays standard in applications of finance and in insurance involving risk aversion. This paper investigates a wide class of risk measures on Orlicz spaces. The characterizing function describes the decision maker's risk assessment towards increasing losses. We link the risk measures to a crucial formula developed by Rockafellar for the Average Value-at-Risk based on convex duality, which is fundamental in corresponding optimization problems. We characterize the dual and provide complementary representations.

This paper investigates the effect of the novel coronavirus and crude oil prices on the United States (US) economic policy uncertainty (EPU). Using daily data for the period January 21-March 13, 2020, our Autoregressive Distributed Lag (ARDL) model shows that the new infection cases reported at global level, and the death ratio, have no significant effect on the US EPU, whereas the oil price negative dynamics leads to increased uncertainty. However, analyzing the situation outside China, we discover that both new case announcements and the COVID-19 associated death ratio have a positive influence on the US EPU.

We consider the problem of the optimal trading strategy in the presence of a price predictor, linear trading costs and a quadratic risk control. The solution is known to be a band system, a policy that induces a no-trading zone in the positions space. Using a path-integral method introduced in a previous work, we give equations for the upper and lower edges of this band, and solve them explicitly in the case of an Ornstein-Uhlenbeck predictor. We then explore the shape of this solution and derive its asymptotic behavior for large values of the predictor, without requiring trading costs to be small.

We analyze an $N+1$-player game and the corresponding mean field game with state space $\{0,1\}$. The transition rate of $j$-th player is the sum of his control $\alpha^j$ plus a minimum jumping rate $\eta$. Instead of working under monotonicity conditions, here we consider an anti-monotone running cost. We show that the mean field game equation may have multiple solutions if $\eta < \frac{1}{2}$. We also prove that that although multiple solutions exist, only the one coming from the entropy solution is charged (when $\eta=0$), and therefore resolve a conjecture of ArXiv: 1903.05788.

This paper studies optimal market making for large-tick assets in the presence of latency. We consider a random walk model for the asset price, and formulate the market maker's optimization problem using Markov Decision Processes (MDP). We characterize the value of an order and show that it plays the role of one-period reward in the MDP model. Based on this characterization, we provide explicit criteria for assessing the profitability of market making when there is latency. Under our model, we show that a market maker can earn a positive expected profit if there are sufficient uninformed market orders hitting the market maker's limit orders compared with the rate of price jumps, and the trading horizon is sufficiently long. In addition, our theoretical and numerical results suggest that latency can be an additional source of risk and latency impacts negatively the performance of market makers.

This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex transport constraints in addition to having given initial and terminal marginals. Several applications are provided: martingale measures with volatility uncertainty, optimal transport with capacity constraints, and Skorokhod embedding with bounded times. Next, we extend this result to multi-marginal constraints. Finally, we consider an optimal transport problem with constraints and obtain its Kantorovich duality. A corollary of this result is a monotonicity principle which gives a geometric way of identifying the optimizer.