Related papers: Binomial approximations of shortfall risk for game…
We study time-inconsistent recursive stochastic control problems, i.e., for which the Bellman principle of optimality does not hold. For this class of problems classical optimal controls may fail to exist, or to be relevant in practice, and…
This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and…
We introduce two-level discounted games played by two players on a perfect-information stochastic game graph. The upper level game is a discounted game and the lower level game is an undiscounted reachability game. Two-level games model…
This paper investigates value function approximation in the context of zero-sum Markov games, which can be viewed as a generalization of the Markov decision process (MDP) framework to the two-agent case. We generalize error bounds from MDPs…
We study a particle approximation for one-dimensional first-order Mean-Field-Games (MFGs) with local interactions with planning conditions. Our problem comprises a system of a Hamilton-Jacobi equation coupled with a transport equation. As…
In this study, we present models where participants strategically select their risk levels and earn corresponding rewards, mirroring real-world competition across various sectors. Our analysis starts with a normal form game involving two…
We compare the option pricing formulas of Louis Bachelier and Black-Merton-Scholes and observe -- theoretically as well as for Bachelier's original data -- that the prices coincide very well. We illustrate Louis Bachelier's efforts to…
We consider the problem of optimal investment with random endowment in a Black--Scholes market for an agent with constant relative risk aversion. Using duality arguments, we derive an explicit expression for the optimal trading strategy,…
We prove a rate of convergence for finite element approximations of stationary, second-order mean field games with nondifferentiable Hamiltonians posed in general bounded polytopal Lipschitz domains with strongly monotone running costs. In…
We begin by reviewing and proving the basic facts of combinatorial game theory. We then consider scoring games (also known as Milnor games or positional games), focusing on the "fixed-length" games for which all sequences of play terminate…
We propose analytical approximations for the sensitivities (Greeks) of the Asian options in the Black-Scholes model, following from a small maturity/volatility approximation for the option prices which has the exact short maturity limit,…
Black-Scholes implied volatility is a quantile. The insight follows from the normalized option price being a probability on the variance scale, with the inverse Gaussian distribution providing the link. It enables analytically exact and…
We consider 2-player stochastic games with perfectly observed actions, and study the limit, as the discount factor goes to one, of the equilibrium payoffs set. In the usual setup where current states are observed by the players, we show…
We propose a projection method to estimate risk-neutral moments from option prices. We derive a finite-sample bound implying that the projection estimator attains (up to a constant) the smallest pricing error within the span of traded…
The Black-Scholes theory of option pricing has been considered for many years as an important but very approximate zeroth-order description of actual market behavior. We generalize the functional form of the diffusion of these systems and…
In the paper written by Klibanov et al, it proposes a novel method to calculate implied volatility of a European stock options as a solution to ill-posed inverse problem for the Black-Scholes equation. In addition, it proposes a trading…
Deep hedging is a framework for hedging derivatives in the presence of market frictions. In this study, we focus on the problem of hedging a given target option by using multiple options. To extend the deep hedging framework to this…
We examine perfect information stochastic mean-payoff games - a class of games containing as special sub-classes the usual mean-payoff games and parity games. We show that deterministic memoryless strategies that are optimal for discounted…
In this paper we solve the discrete time mean-variance hedging problem when asset returns follow a multivariate autoregressive hidden Markov model. Time dependent volatility and serial dependence are well established properties of financial…
The projection games (aka Label-Cover) problem is of great importance to the field of approximation algorithms, since most of the NP-hardness of approximation results we know today are reductions from Label-Cover. In this paper we design…