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We study an agent-based stock market model with heterogeneous agents and friction. Our model is based on that of Foellmer-Schweizer(1993): The process of a stock price in a discrete-time framework is determined by temporary equilibria via…

Probability · Mathematics 2013-01-29 Takashi Kato

We study a model of moral hazard with heterogeneous beliefs where each of agent's actions gives rise to a pair of probability distributions over output levels, one representing the beliefs of the agent and the other those of the principal.…

Theoretical Economics · Economics 2021-10-12 Martin Dumav , Urmee Khan , Luca Rigotti

This paper investigates portfolio selection within a continuous-time financial market with regime-switching and beliefs-dependent utilities. The market coefficients and the investor's utility function both depend on the market regime, which…

Optimization and Control · Mathematics 2024-10-23 Xiaochen Chen , Guohui Guan , Zongxia Liang

We consider the pricing and hedging of exotic options in a model-independent set-up using \emph{shortfall risk and quantiles}. We assume that the marginal distributions at certain times are given. This is tantamount to calibrating the model…

Pricing of Securities · Quantitative Finance 2013-07-10 Erhan Bayraktar , Zhou Zhou

The paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of martingale-like properties as well as a…

Mathematical Finance · Quantitative Finance 2015-11-06 Sebastian E. Ferrando , Alfredo L. Gonzalez , Ivan L. Degano , Massoome Rahsepar

We define and study a rather complex market model, inspired from the Santa Fe artificial market and the Minority Game. Agents have different strategies among which they can choose, according to their relative profitability, with the…

Condensed Matter · Physics 2009-11-07 Irene Giardina , Jean-Philippe Bouchaud

We study partial hedging for game options in markets with transaction costs bounded from below. More precisely, we assume that the investor's transaction costs for each trade are the maximum between proportional transaction costs and a…

Mathematical Finance · Quantitative Finance 2015-06-08 Yan Dolinsky , Yuri Kifer

We propose two rational expectation models of transient financial bubbles with heterogeneous arbitrageurs and positive feedbacks leading to self-reinforcing transient stochastic faster-than-exponential price dynamics. As a result of the…

General Finance · Quantitative Finance 2009-11-11 Li Lin , Didier Sornette

We study a variant of the martingale optimal transport problem in a multi-period setting to derive robust price bounds of a financial derivative. On top of marginal and martingale constraints, we introduce a time-homogeneity assumption,…

Mathematical Finance · Quantitative Finance 2021-05-07 Stephan Eckstein , Michael Kupper

This paper studies the model risk of the Black-Scholes (BS) model in pricing and risk-managing variable annuities motivated by its wide usage in the insurance industry. Specifically, we derive a model-free decomposition of the no-arbitrage…

Mathematical Finance · Quantitative Finance 2022-08-30 Zhiyi Shen

Prediction markets mobilize financial incentives to forecast binary event outcomes through the aggregation of dispersed beliefs and heterogeneous information. Their growing popularity and demonstrated predictive accuracy in political…

General Economics · Economics 2026-01-29 Bridget Smart , Ebba Mark , Anne Bastian , Josefina Waugh

Considering a simple economy, we derive a new Hamilton-Jacobi equation which is satisfied by the value of a ''bubble'' asset. We then show, by providing a rigorous mathematical analysis of this equation, that a unique non-zero stable…

Analysis of PDEs · Mathematics 2025-05-22 Charles Bertucci , Jean-Michel Lasry , Pierre Louis Lions

We model an informed agent with information about the future value of an asset trying to maximize profits when subjected to a transaction cost as well as a market maker tasked with setting fair transaction prices. In a single auction model,…

Trading and Market Microstructure · Quantitative Finance 2020-07-29 Weston Barger , Ryan Donnelly

We design three continuous--time models in finite horizon of a commodity price, whose dynamics can be affected by the actions of a representative risk--neutral producer and a representative risk--neutral trader. Depending on the model, the…

Mathematical Finance · Quantitative Finance 2020-03-04 René Aïd , Giorgia Callegaro , Luciano Campi

The thesis of this essay is that, in heterogeneous agent macroeconomics, the assumption of rational expectations about equilibrium prices is unrealistic and should be replaced. Rational expectations imply that decision makers forecast…

General Economics · Economics 2025-08-29 Benjamin Moll

We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean-revert around their…

Mathematical Finance · Quantitative Finance 2020-04-16 Lukas Gonon , Johannes Muhle-Karbe , Xiaofei Shi

A common assumption in financial engineering is that the market price for any derivative coincides with an objectively defined risk-neutral price - a plausible assumption only if traders collectively possess objective knowledge about the…

Pricing of Securities · Quantitative Finance 2013-10-08 Kerry W. Fendick

We consider a multi-asset incomplete model of the financial market, where each of $m\geq 2$ risky assets follows the binomial dynamics, and no assumptions are made on the joint distribution of the risky asset price processes. We provide…

Mathematical Finance · Quantitative Finance 2024-05-09 Jarek Kędra , Assaf Libman , Victoria Steblovskaya

An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an $\alpha$-maxmin nonlinear…

Mathematical Finance · Quantitative Finance 2021-07-15 Yu-Jui Huang , Xiang Yu

American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale…

Pricing of Securities · Quantitative Finance 2008-12-02 Alet Roux , Tomasz Zastawniak