Adachi and Ryu introduced a category Prob of probability spaces whose objects are all probability spaces and whose arrows correspond to measurable functions satisfying an absolutely continuous requirement in [Adachi and Ryu, 2019]. In this paper, we develop a binomial asset pricing model based on Prob. We introduce generalized filtrations with which we can represent situations such as some agents forget information at some specific time. We investigate the valuations of financial claims along this type of non-standard filtrations.

Examining the topological properties of networks formed by such guarantee relationships is critical for an in-depth understanding and effective regulations of the financial system. In this research, we analyzed the structure and evolution of the Chinese guarantee network with real-world data from 2007 to 2012. We identified the scale-free and power-law properties of the guarantee network and found the global financial crisis and follow-up economic stimulus program had a significant influence on the evolution of the guarantee network. In particular, both the growth and connectivity of the guarantee network was diminished by the 2008 financial crisis, and enhanced by the following stimulus program. This research presents data-driven insights on how the topological structure of the guarantee network is associated with economic policies.

In recent decades, in developed economies, slack on the product and labor markets has fluctuated a lot over the business cycle, while inflation has been very stable. At the same time, these economies have been prone to enter long-lasting liquidity traps with stable positive inflation and high unemployment. Motivated by these observations, this paper develops a simple policy-oriented business-cycle model in which (1) fluctuations in aggregate demand and supply lead to fluctuations in slack but not in inflation; and (2) the aggregate demand structure is consistent with permanent liquidity traps. The model extends the money-in-the-utility-function model by introducing matching frictions and including real wealth into the utility function. Matching frictions allow us to represent slack and to consider a general equilibrium with constant inflation. Wealth in the utility function enriches the aggregate demand structure to be consistent with permanent liquidity traps. We use the model to study the effects of various aggregate demand and supply shocks, and to analyze several stabilization policies---such as conventional monetary policy, helicopter drop of money, tax on wealth, and government spending.

In this paper we explore the usage of deep reinforcement learning algorithms to automatically generate consistently profitable, robust, uncorrelated trading signals in any general financial market. In order to do this, we present a novel Markov decision process (MDP) model to capture the financial trading markets. We review and propose various modifications to existing approaches and explore different techniques like the usage of technical indicators, to succinctly capture the market dynamics to model the markets. We then go on to use deep reinforcement learning to enable the agent (the algorithm) to learn how to take profitable trades in any market on its own, while suggesting various methodology changes and leveraging the unique representation of the FMDP (financial MDP) to tackle the primary challenges faced in similar works. Through our experimentation results, we go on to show that our model could be easily extended to two very different financial markets and generates a positively robust performance in all conducted experiments.

We propose a novel approach for sampling realistic financial correlation matrices. This approach is based on generative adversarial networks. Experiments demonstrate that generative adversarial networks are able to recover most of the known stylized facts about empirical correlation matrices estimated on asset returns. This is the first time such results are documented in the literature. Practical financial applications range from trading strategies enhancement to risk and portfolio stress testing. Such generative models can also help ground empirical finance deeper into science by allowing for falsifiability of statements and more objective comparison of empirical methods.

This is the first study that attempts to assess the regional economic impacts of the European Institute of Innovation and Technology (EIT) investments in a spatially explicit macroeconomic model, which allows us to take into account all key direct, indirect and spatial spillover effects of EIT investments via inter-regional trade and investment linkages and a spatial diffusion of technology via an endogenously determined global knowledge frontier with endogenous growth engines driven by investments in knowledge and human capital. Our simulation results of highly detailed EIT expenditure data suggest that, besides sizable direct effects in those regions that receive the EIT investment support, there are also significant spatial spillover effects to other (non-supported) EU regions. Taking into account all key indirect and spatial spillover effects is a particular strength of the adopted spatial general equilibrium methodology; our results suggest that they are important indeed and need to be taken into account when assessing the impacts of EIT investment policies on regional economies.

We suggest a simple reduction of pricing European options in affine jump-diffusion models to pricing options with modified payoffs in diffusion models. The procedure is based on the conjugation of the infinitesimal generator of the model with an operator of the form $e^{i\Phi(-i\dd_x)}$ (gauge transformation in the dual space). A general procedure for the calculation of the function $\Phi$ is given, with examples. As applications, we consider pricing in jump-diffusion models and their subordinated versions using the eigenfunction expansion technique, and estimation of the extremely rare jumps component. The beliefs of the market about yet unobserved extreme jumps and pricing kernel and can be recovered: the market prices allow one to see "the shape of things to come".

The indirect transactions between sectors of an economic system has been a long-standing open problem. There have been numerous attempts to define and mathematically formulate this concept in various other scientific fields in literature as well. The existing indirect effects formulations, however, cannot quantify the indirect interactions and transactions between any two sectors of an economic system. Therefore, although the direct and total requirement matrices are formulated and used for economic system analysis, the indirect requirements matrices has never been formulated before. Based on the system decomposition theory, the indirect transactions between two sectors of an economic system and the corresponding indirect requirements matrices are introduced in the present article for the first time. This novel concept of the indirect transactions is also compared with some existing indirect effect formulations, and the theoretical advancements brought by the proposed methodology are discussed. It is shown theoretically and through illustrative examples that the proposed indirect transactions accurately describe and quantify the indirect interactions and transactions, unlike the current indirect effects formulations. The indirect requirements matrices for the US economy using aggregated input-output tables for multiple years are also presented and briefly analyzed.

This paper studies a mean-variance portfolio selection problem under partial information with drift uncertainty. It is proved that all the contingent claims in this model are attainable in the sense of Xiong and Zhou. Further, we propose a numerical scheme to approximate the optimal portfolio. Malliavin calculus and the strong law of large numbers play important roles in this scheme.

In this study, we investigate the evolution of Chinese guarantee networks from the angle of sub-patterns. First, we find that the mutual, 2-out-stars and triangle sub-patterns are motifs in 2- and 3-node subgraphs. Considering the heterogeneous financial characteristics of nodes, we find that small firms tend to form a mutual guarantee relationship and large firms are likely to be the guarantors in 2-out-stars sub-patterns.

The pricing of Bermudan options amounts to solving a dynamic programming principle, in which the main difficulty, especially in high dimension, comes from the conditional expectation involved in the computation of the continuation value. These conditional expectations are classically computed by regression techniques on a finite dimensional vector space. In this work, we study neural networks approximations of conditional expectations. We prove the convergence of the well-known Longstaff and Schwartz algorithm when the standard least-square regression is replaced by a neural network approximation. We illustrate the numerical efficiency of neural networks as an alternative to standard regression methods for approximating conditional expectations on several numerical examples.

This paper deals with the efficient numerical solution of the two-dimensional partial integro-differential complementarity problem (PIDCP) that holds for the value of American-style options under the two-asset Merton jump-diffusion model. We consider the adaptation of various operator splitting schemes of both the implicit-explicit (IMEX) and the alternating direction implicit (ADI) kind that have recently been studied for partial integro-differential equations (PIDEs) in [3]. Each of these schemes conveniently treats the nonlocal integral part in an explicit manner. Their adaptation to PIDCPs is achieved through a combination with the Ikonen-Toivanen splitting technique [14] as well as with the penalty method [32]. The convergence behaviour and relative performance of the acquired eight operator splitting methods is investigated in extensive numerical experiments for American put-on-the-min and put-on-the-average options.

Predicting the intraday stock jumps is a significant but challenging problem in finance. Due to the instantaneity and imperceptibility characteristics of intraday stock jumps, relevant studies on their predictability remain limited. This paper proposes a data-driven approach to predict intraday stock jumps using the information embedded in liquidity measures and technical indicators. Specifically, a trading day is divided into a series of 5-minute intervals, and at the end of each interval, the candidate attributes defined by liquidity measures and technical indicators are input into machine learning algorithms to predict the arrival of a stock jump as well as its direction in the following 5-minute interval. Empirical study is conducted on the level-2 high-frequency data of 1271 stocks in the Shenzhen Stock Exchange of China to validate our approach. The result provides initial evidence of the predictability of jump arrivals and jump directions using level-2 stock data as well as the effectiveness of using a combination of liquidity measures and technical indicators in this prediction. We also reveal the superiority of using random forest compared to other machine learning algorithms in building prediction models. Importantly, our study provides a portable data-driven approach that exploits liquidity and technical information from level-2 stock data to predict intraday price jumps of individual stocks.

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from Pontryagin's stochastic maximum principle. Although the same cost functions as well as the coefficient functions of the state dynamics are shared among the agents within each population, they can be different population by population. We study the mean field limit for the three different situations; (i) every agent is non-cooperative; (ii) the agents within each population are cooperative; and (iii) the agents in some populations are cooperative but those in the other populations are not. We provide several sets of sufficient conditions for the existence of a mean field equilibrium for each of these cases. Furthermore, under appropriate conditions, we show that the mean field solution to each of these problems actually provides an approximate Nash equilibrium for the corresponding game with a large but finite number of agents.

In this paper we perform robustness and sensitivity analysis of several continuous-time stochastic volatility (SV) models with respect to the process of market calibration. The analyses should validate the hypothesis on importance of the jump part in the underlying model dynamics. Also an impact of the long memory parameter is measured for the approximative fractional SV model. For the first time, the robustness of calibrated models is measured using bootstrapping methods on market data and Monte-Carlo filtering techniques. In contrast to several other sensitivity analysis approaches for SV models, the newly proposed methodology does not require independence of calibrated parameters - an assumption that is typically not satisfied in practice. Empirical study is performed on data sets of Apple Inc. equity options traded in April and May 2015.

We prove a scaling limit theorem for the super-replication cost of options in a Cox--Ross--Rubinstein binomial model with transient price impact. The correct scaling turns out to keep the market depth parameter constant while resilience over fixed periods of time grows in inverse proportion with the duration between trading times. For vanilla options, the scaling limit is found to coincide with the one obtained by PDE methods in [12] for models with purely temporary price impact. These models are a special case of our framework and so our probabilistic scaling limit argument allows one to expand the scope of the scaling limit result to path-dependent options.

Scalar dynamic risk measures in continuous time are commonly represented as backward stochastic differential equations. There are two possible extensions for scalar backward stochastic differential equations for the set-valued framework: (1) backward stochastic differential inclusions; or (2) set-valued backward stochastic differential equations. In this work, the discrete-time setting is investigated with difference inclusions and difference equations in order to provide insights for such differential representations for set-valued dynamic risk measures.

We provide existence, uniqueness and stability results for affine stochastic Volterra equations with $L^1$-kernels. Such equations arise as scaling limits of branching processes in population genetics and self-exciting Hawkes processes in mathematical finance. The strategy we adopt for the existence part is based on approximations using stochastic Volterra equations with $L^2$-kernels. Most importantly, we establish weak uniqueness using a duality argument on the Fourier-Laplace transform via a deterministic Riccati-Volterra integral equation. We illustrate the applicability of our results on a class of hyper-rough Volterra Heston models with a Hurst index $H \in (-1/2, 1/2]$.