arXiv research

Investors' strategic trading affects asset prices, modeled as a game.

We study a robust Dynkin game over a set of mutually singular probabilities. We first prove that for the conservative player of the game, her lower and upper value processes coincide (i.e. She has a value process $V$ in the game). Such a result helps people connect the robust Dynkin game with second-order doubly refle…

Deep fictitious play converges to Nash equilibrium in stochastic differential games.

The paper solves investment problems with uncertain factors using game theory.

The paper solves TIC LQ control problems using stochastic differential games.

Paper proves existence and uniqueness of solutions to nonlocal systems, generalizing stochastic game theory.

Study on games with degenerate diffusion matrices, proving value existence and convergence.

This paper presents a novel approach to numerically solve stochastic differential games for nonlinear systems. The proposed approach relies on the nonlinear Feynman-Kac theorem that establishes a connection between parabolic deterministic partial differential equations and forward-backward stochastic differential equat…

Solves a game between brokers and informed traders using stochastic differential equations.

Paper solves complex game theory problems with new equations.

This paper studies insurers' robust strategies in a stochastic game with model uncertainty and volatility risk.

Study improves $L^{\infty}$ estimates and extreme value behavior in stochastic differential games.

Study competitive energy markets using stochastic impulse games.

We consider a general time-inconsistent stochastic linear-quadratic differential game. The time-inconsistency arises from the presence of quadratic terms of the expected state as well as state-dependent term in the objective functionals. We define an equilibrium strategy, which is different from the classical one, and …

In this paper we propose and analyze a class of $N$-player stochastic games that include finite fuel stochastic games as a special case. We first derive sufficient conditions for the Nash equilibrium (NE) in the form of a verification theorem. The associated Quasi-Variational-Inequalities include an essential game comp…

We consider a stochastic game of contribution to the common good in which the players have continuous control over the degree of contribution, and we examine the gradualism arising from the free rider effect. This game belongs to the class of variable concession games which generalize wars of attrition. Previously know…

Proposes a deep learning method for solving complex financial games with delays.

Game theory models how agents trade in a risky asset considering price impact and a common signal.

Two firms compete in a financial market, choosing dividend strategies to avoid default and maximize profits.

This paper investigates a hybrid stochastic differential reinsurance and investment game between one reinsurer and two insurers, including a stochastic Stackelberg differential subgame and a non-zero-sum stochastic differential subgame. The reinsurer, as the leader of the Stackelberg game, can price reinsurance premium…

In this paper, we apply the idea of fictitious play to design deep neural networks (DNNs), and develop deep learning theory and algorithms for computing the Nash equilibrium of asymmetric $N$-player non-zero-sum stochastic differential games, for which we refer as \emph{deep fictitious play}, a multi-stage learning pro…

The paper extends macroscopic market making to stochastic games, revealing properties and solving equations.

The paper analyzes reinsurance strategies in a competitive multi-agent system.

We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the volatility terms of the state process. Under appropriate conditions, we show that t…

Model predicts BESS interactions and price impacts in energy markets.

We develop an option pricing model based on a tug-of-war game. This two-player zero-sum stochastic differential game is formulated in the context of a multi-dimensional financial market. The issuer and the holder try to manipulate asset price processes in order to minimize and maximize the expected discounted reward. W…

In this article we consider a game theoretic approach to the Risk-Sensitive Benchmarked Asset Management problem (RSBAM) of Davis and Lleo \cite{DL}. In particular, we consider a stochastic differential game between two players, namely, the investor who has a power utility while the second player represents the market …

Two neural network methods solve the master equation for MFGs.

The study examines how brokers' identity affects their trading strategies on the Toronto Stock Exchange.

Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform optimal execution or statistical arbitrage, where all agents filter the latent states of the world, and their trading actions hav…

Study on mean field games with singular controls and their applications.

Recent results and interpretations are presented for the thermal minority game, concentrating on deriving and justifying the fundamental stochastic differential equation for the microdynamics.

Study shows how multiple traders can trade together without excessive price impact.

Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading actions. The market has latent factors that drive prices, and agents account for th…

This paper analyzes a class of infinite-time-horizon stochastic games with singular controls motivated from the partially reversible problem. It provides an explicit solution for the mean-field game (MFG) and presents sensitivity analysis to compare the solution for the MFG with that for the single-agent control proble…

We analyze a market impact game between $n$ risk averse agents who compete for liquidity in a market impact model with permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. Our first main result characterizes the Nash equilibrium in t…

This paper optimizes trading strategies to minimize risk and maximize profit while accounting for market uncertainty.

Model strategic interactions between market makers and traders to optimize execution.

The existence of stationary Markov perfect equilibria in stochastic games is shown under a general condition called "(decomposable) coarser transition kernels". This result covers various earlier existence results on correlated equilibria, noisy stochastic games, stochastic games with finite actions and state-independe…

This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's value to be continuous with respect to the time horizon are obtained using recent …

Study on optimal trading in a finite population with market frictions and asymmetric information.

We propose a model of inter-bank lending and borrowing which takes into account clearing debt obligations. The evolution of log-monetary reserves of $N$ banks is described by coupled diffusions driven by controls with delay in their drifts. Banks are minimizing their finite-horizon objective functions which take into a…

Modeling market makers' quoting strategies to understand price impact.

In this paper we are concerned with backward stochastic differential equations with random default time and their applications to default risk. The equations are driven by Brownian motion as well as a mutually independent martingale appearing in a defaultable setting. We show that these equations have unique solutions …

The paper analyzes strategic interactions in a multi-agent reinsurance chain using game theory.

For a monotonically advancing front, the arrival time is the time when the front reaches a given point. We show that it is twice differentiable everywhere with uniformly bounded second derivative. It is smooth away from the critical points where the equation is degenerate. We also show that the critical set has finite …

We consider the problem of finding stationary Nash equilibria (NE) in a finite discounted general-sum stochastic game. We first generalize a non-linear optimization problem from Filar and Vrieze [2004] to a $N$-player setting and break down this problem into simpler sub-problems that ensure there is no Bellman error fo…

(Working Paper) Using a purely probabilistic argument, we prove the global well-posedness of multidimensional superquadratic backward stochastic differential equations (BSDEs) without Markovian assumption. The key technique is the interplay between the local well-posedness of fully coupled path-dependent forward backwa…