We solve the problem of valuing and optimal exercise of American call-type options in markets which do not necessarily admit an equivalent local martingale measure. This resolves an open question proposed by Karatzas and Fernholz (Handbook of Numerical Analysis, vol. 15, pp. 89–167, Elsevier,...

We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of the state space. We allow for various types of model...

This paper introduces a dual problem to study a continuous-time consumption and investment problem with incomplete markets and Epstein-Zin stochastic differential utility. Duality between the primal and dual problems is established. Consequently the optimal strategy of this consumption and...

We consider the problem of finding equilibrium asset prices in a financial market in which a portfolio manager (Agent) invests on behalf of an investor (Principal), who compensates the manager with an optimal contract. We extend a model from Buffa, Vayanos and Woolley (2014) by allowing general...

We study existence and uniqueness of continuous-time stochastic Radner equilibria in an incomplete markets model. An assumption of "smallness'' type - imposed through the new notion of "closeness to Pareto optimality'' - is shown to be sufficient for existence and uniqueness. Central role in our...