We analyze a macroeconomic model with intergenerational equity considerations and spatial spillovers, which gives rise to a multicriteria optimization problem. Intergenerational equity requires to add in the definition of social welfare a long run sustainability criterion to the traditional discounted utilitarian criterion. The spatial structure allows for the possibility of heterogeneiity and spatial diffusion implies that all locations within the spatial domain are interconnected via spatial spillovers. We rely on different techniques (scalarization, $\epsilon$-constraint method and goal programming) to analyze such a spatial multicriteria problem, relying on numerical approaches to illustrate the nature of the trade-off between the discounted utilitarian and the sustainability criteria.

We propose a mathematical model of momentum risk-taking, which is real-time risk management, and discuss its implementation: an automated momentum equity trading system. Risk-taking is one of the key components of general decision-making, a challenge for artificial intelligence and machine learning. We begin with a simple continuous model of news impact and then perform its discretization, adjusting it to dealing with discontinuous functions. Stock charts are the main examples for us; stock markets are quite a test for any risk management theories. An entirely automated trading system based on our approach proved to be successful in extensive historical and real-time experiments. Its preimage is a new contract card game presented at the end of the paper.

Periodic Double Auctions (PDAs) are commonly used in the real world for trading, e.g. in stock markets to determine stock opening prices, and energy markets to trade energy in order to balance net demand in smart grids, involving trillions of dollars in the process. A bidder, participating in such PDAs, has to plan for bids in the current auction as well as for the future auctions, which highlights the necessity of good bidding strategies. In this paper, we perform an equilibrium analysis of single unit single-shot double auctions with a certain clearing price and payment rule, which we refer to as ACPR, and find it intractable to analyze as number of participating agents increase. We further derive the best response for a bidder with complete information in a single-shot double auction with ACPR. Leveraging the theory developed for single-shot double auction and taking the PowerTAC wholesale market PDA as our testbed, we proceed by modeling the PDA of PowerTAC as an MDP. We propose a novel bidding strategy, namely MDPLCPBS. We empirically show that MDPLCPBS follows the equilibrium strategy for double auctions that we previously analyze. In addition, we benchmark our strategy against the baseline and the state-of-the-art bidding strategies for the PowerTAC wholesale market PDAs, and show that MDPLCPBS outperforms most of them consistently.

Using the most comprehensive source of commercially available data on the US National Market System, we analyze all quotes and trades associated with Dow 30 stocks in 2016 from the vantage point of a single and fixed frame of reference. We find that inefficiencies created in part by the fragmentation of the equity marketplace are relatively common and persist for longer than what physical constraints may suggest. Information feeds reported different prices for the same equity more than 120 million times, with almost 64 million dislocation segments featuring meaningfully longer duration and higher magnitude. During this period, roughly 22% of all trades occurred while the SIP and aggregated direct feeds were dislocated. The current market configuration resulted in a realized opportunity cost totaling over $160 million when compared with a single feed, single exchange alternative---a conservative estimate that does not take into account intra-day offsetting events.

In this paper, we present the testing of four hypotheses on two streams of observations that are driven by L\'evy processes. This is applicable for sequential decision making on the state of two-sensor systems. In one case, each sensor receives or does not receive a signal obstructed by noise. In another, each sensor receives data-driven by L\'evy processes with large or small jumps. In either case, these give rise to four possibilities. Infinitesimal generators are presented and analyzed. Bounds for infinitesimal generators in terms of \emph{super-solutions} and \emph{sub-solutions} are computed. An application of this procedure for the stochastic model is also presented in relation to the financial market.

We propose a class of financial models in which the prices of assets are L\'evy-Ito processes driven by Brownian motion and a dynamic Poisson random measure. Each such model consists of a pricing kernel, a money market account, and one or more risky assets. The Poisson random measure is associated with an $n$-dimensional L\'evy process. We show that the excess rate of return of a risky asset in a pure-jump model is given by an integral of the product of a term representing the riskiness of the asset and a term representing the level of market risk aversion. The integral is over the state space of the Poisson random measure and is taken with respect to the L\'evy measure associated with the $n$-dimensional L\'evy process. The resulting framework is applied to a variety of different asset classes, allowing one to construct new models as well as non-trivial generalizations of familiar models.

This paper investigates Merton's portfolio problem in a rough stochastic environment described by Volterra Heston model. The model has a non-Markovian and non-semimartingale structure. By considering an auxiliary random process, we solve the portfolio optimization problem with the martingale optimality principle. Optimal strategies for power and exponential utilities are derived in semi-closed form solutions depending on the respective Riccati-Volterra equations. We numerically examine the relationship between investment demand and volatility roughness.