Two major financial market complexities are transaction costs and uncertain volatility, and we analyze their joint impact on the problem of portfolio optimization. When volatility is constant, the transaction costs optimal investment problem has a long history, especially in the use of...

This supplemental appendix accompanies "Optimal Investment with Transaction Costs and Stochastic Volatility Part II: Finite Horizon" by the same authors, available at:"http://ssrn.com/abstract=2659918" http://ssrn.com/abstract=2659918. In this appendix we prove the verification theorem that the...

In this companion paper to “Optimal Investment with Transaction Costs and Stochastic Volatility Part I: Infinite Horizon”, "http://ssrn.com/abstract=2374150" http://ssrn.com/abstract=2374150, we give an accuracy proof for the finite time optimal investment and consumption problem under fast...

We develop a novel framework for computing the total valuation adjustment (XVA) of a European claim accounting for funding costs, counterparty credit risk, and collateralization. Based on no-arbitrage arguments, we derive the nonlinear backward stochastic differential equations (BSDEs)...

We study the semilinear partial differential equation (PDE) associated with the non-linear BSDE characterizing buyer's and seller's XVA in a framework that allows for asymmetries in funding, repo and collateral rates, as well as for early contract termination due to counterparty credit risk. We...

We consider the terminal wealth utility maximization problem from the point of view of a portfolio manager who is paid by an incentive scheme, which is given as a convex function $g$ of the terminal wealth. The manager's own utility function $U$ is assumed to be smooth and strictly concave,...

We consider an agent who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of a proportional transaction cost. The utility function considered is power utility. We provide a heuristic and a rigorous...

We price a contingent claim liability using the utility indifference argument. We consider an agent with exponential utility, who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of positive proportional...

Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar and S{\o}lna (2011, CUP) analyzes models in which the...

We study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein-Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that takes a log-Brownian motion to describe price dynamics...