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We model stochastic choice as environment-dependent switching among a small library of deterministic decision rules. A Random Rule Model generates menu-level choice probabilities via named, interpretable rules weighted by observable menu…
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…
We propose a simple statistical-physics-inspired model for the effect of intrinsic fluctuations on supply and demand in markets. The model consists of agents that trade in two types of goods of which the total number is separately…
We show that the frequent claim that the implied tree prices exotic options consistently with the market is untrue if the local volatilities are subject to change and the market is arbitrage-free. In the process, we analyse -- in the most…
We present a numerically efficient approach for learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be…
The Black-Scholes model (sometimes known as the Black-Scholes-Merton model) gives a theoretical estimate for the price of European options. The price evolution under this model is described by the Black-Scholes formula, one of the most…
We construct and study market models admitting optimal arbitrage. We say that a model admits optimal arbitrage if it is possible, in a zero-interest rate setting, starting with an initial wealth of 1 and using only positive portfolios, to…
In this paper, we study the asymptotic behavior of Asian option prices in the worst case scenario under an uncertain volatility model. We give a procedure to approximate the Asian option prices with a small volatility interval. By imposing…
The space of call price functions has a natural noncommutative semigroup structure with an involution. A basic example is the Black--Scholes call price surface, from which an interesting inequality for Black--Scholes implied volatility is…
The multidimensional Uncertain Volatility Model leads to robust option pricing problems under joint volatility and correlation uncertainty. Their numerical resolution quickly becomes challenging because the associated stochastic control…
We construct an equilibrium for the continuous time Kyle's model with stochastic liquidity, a general distribution of the fundamental price, and correlated stock and volatility dynamics. For distributions with positive support, our…
Based on a criterion of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity…
This paper deals with asset price bubbles modeled by strict local martingales. With any strict local martingale, one can associate a new measure, which is studied in detail in the first part of the paper. In the second part, we determine…
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…
Although behavioral economics has demonstrated that there are many situations where rational choice is a poor empirical model, it has so far failed to provide quantitative models of economic problems such as price formation. We make a step…
Predicting volatility is important for asset predicting, option pricing and hedging strategies because it cannot be directly observed in the financial market. The Black-Scholes option pricing model is one of the most widely used models by…
We give a new formulation of the relative arbitrage problem from stochastic portfolio theory that asks for a time horizon beyond which arbitrage relative to the market exists in all ``sufficiently volatile'' markets. In our formulation,…
A master equation approach to the numerical solution of option pricing models is developed. The basic idea of the approach is to consider the Black--Scholes equation as the macroscopic equation of an underlying mesoscopic stochastic option…
In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and…
A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…