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We consider existence and uniqueness of Nash equilibria in an $N$-player game of utility maximization under relative performance criteria of multiplicative form in complete semimartingale markets. For a large class of players' utility…
This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes.…
We consider a multivariate financial market with transaction costs and study the problem of finding the minimal initial capital needed to hedge, without risk, European-type contingent claims. The model is similar to the one considered in…
In exponential semi-martingale setting for risky asset we estimate the difference of prices of options when initial physical measure $P$ and corresponding martingale measure $Q$ change to $\tilde{P}$ and $\tilde{Q}$ respectively. Then, we…
The goal of an auction is to determine commodity prices such that all participants are perfectly happy. Such a solution is called a competitive equilibrium and does not exist in general. For this reason we are interested in solutions which…
This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes.…
We present a mathematical model of a market with $m$ shares traded across $n$ investor groups, each one with similar motivations and trading strategies. The market of each asset consists of a fixed amount of cash and shares (no additions…
We investigate a Kyle model under Gaussian assumptions where a risk-averse informed trader has imperfect information on the fundamental price of an asset. We show that an equilibrium can be constructed by considering an optimal transport…
Given two probability measures on sequential data, we investigate the transport problem with time-inconsistent preferences in a discrete-time setting. Motivating examples are nonlinear objectives, state-dependent costs, and regularized…
We propose a pricing technique based on coherent risk measures, which enables one to get finer price intervals than in the No Good Deals pricing. The main idea consists in splitting a liability into several parts and selling these parts to…
We analyze a continuous time multidimensional opinion model where agents have heterogeneous but symmetric and compactly supported interaction functions. We consider Filippov solutions of the resulting dynamics and show strong Lyapunov…
When uncertainty is modelled by a set of non-dominated and non-compact probability measures, a notion of essential supremum for a family of real-valued functions is developed in terms of upper semi-analytic functions. We show how the…
I study the limit of a large random economy, where a set of consumers invests in financial instruments engineered by banks, in order to optimize their future consumption. This exercise shows that, even in the ideal case of perfect…
In many first-price auctions, bidders face considerable strategic uncertainty: They cannot perfectly anticipate the other bidders' bidding behavior. We propose a model in which bidders do not know the entire distribution of opponent bids…
We derive the arbitrage gains or, equivalently, Loss Versus Rebalancing (LVR) for arbitrage between \textit{two imperfectly liquid} markets, extending prior work that assumes the existence of an infinitely liquid reference market. Our…
We consider a financial market model with a single risky asset whose price process evolves according to a general jump-diffusion with locally bounded coefficients and where market participants have only access to a partial information flow.…
This paper considers finitely many investors who perform mean-variance portfolio selection under relative performance criteria. That is, each investor is concerned about not only her terminal wealth, but how it compares to the average…
We consider the optimal investment and marginal utility pricing problem of a risk averse agent and quantify their exposure to a small amount of model uncertainty. Specifically, we compute explicitly the first-order sensitivity of their…
We consider two sided matching markets consisting of agents with non-transferable utilities; agents from the opposite sides form matching pairs (e.g., buyers-sellers) and negotiate the terms of their math which may include a monetary…
We propose a decentralized market model in which agents can negotiate bilateral contracts. This builds on a similar, but centralized, model of trading networks introduced by Hatfield et al. in 2013. Prior work has established that…