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A Stochastic Model of Optimal Debt Management and BankruptcyÌýWe consider a problem of optimal debt management which is modeled as a non-cooperative game between a borrower and a pool of risk-neutral lenders. Since the debtor may go bankrupt,

Optimal Consumption in the Stochastic Ramsey Problem without Boundedness ConstraintsÌýThis paper investigates optimal consumption in the stochastic Ramsey problem with the Cobb-Douglas production function. Contrary to prior studies, we allow for

Epstein-Zin Utility Maximization over Random HorizonÌýThis talk focuses on solving the consumption-investment problem for an agent withÌýstochastic differential utilityÌýof Epstein-Zin type. In contrast to prior literature, our time

American option pricing under stochastic volatility models via Picard iterationsÌýThis talk discusses the valuation of American options for a general one- factor stochastic volatility model. Using the local time-space calculus on surfaces we

Optimal Portfolio under Fractional Stochastic Environments Rough stochastic volatility models have attracted a lot of attention recently, in particular for the linear option pricing problem. In this paper, starting with power utilities, we propose

Nonzero-sum stochastic differential games with impulse controls We consider a general class of nonzero-sum impulsive games with N players. By means of a suitable system of quasi-variationalÌý inequalities, we provide a verification theorem for

The Value of Scattered InformationWe analyze a model in which the value of a security is comprised of multiple distinct parts and private information about these pieces is scattered among investors. We show that as information is scattered into

Machine Learning in Quantitative FinanceMachine learning has revolutionized fields such as image, text, and speech recognition. There is now growing interest in applying machine learning in financial applications. Recently, we have developed machine

Portfolios, optimal transport and informations geometryCan we outperform a market index in the presence of volatility? What is the optimal frequency to rebalance a portfolio? We show that these questions can be analyzed using modern ideas in

A Dynamic Equilibrium Model for Brokerage FeesWeÌý develop a dynamic equilibrium model for market liquidity. To wit, we solve for the equilibrium prices at which liquidity takers' demands are absorbed by liquidity providers, who can in turn