We present efficient partial differential equation (PDE) methods for continuous time mean-variance portfolio allocation problems when the underlying risky asset follows a jump-diffusion. The standard formulation of mean-variance optimal portfolio allocation problems, where the total wealth is...

Investors often control risk exposure by trading options. This article studies the optimal strategy for liquidating an option position. Under both complete and incomplete market settings, we quantify the value of optimally timing to liquidate, and identify the situations where it is optimal to...

This article establishes the Poisson optional stopping times (POST) method by [22] as a near-universal method for solving liquidity-constrained American options, or, equivalently, penalised optimal-stopping problems. In this setup, the decision maker is permitted to "stop", i.e. exercise the...

Calibrating option pricing models to market prices often leads to optimisation problems to which standard methods (like such based on gradients) cannot be applied. We investigate two models: Heston's stochastic volatility model, and Bates's model which also includes jumps. We discuss how to...

We study optimal investment with multiple assets in the presence of small proportional transaction costs. Rather than computing an asymptotically optimal no-trade region, we optimize over suitable trading frequencies. We derive explicit formulas for these and the associated welfare losses due to...

This paper presents the theoretical and applicative model elaborated by Harry Markowitz on the determination of the structure of the efficient securities portfolio. In this sense, in order to determine the structure of the efficient Markowitz portfolio (PE), a Lagrange function is built and...

We study the continuous time portfolio selection problem over a finite horizon for an investor who maximizes the expected utility of terminal wealth and faces transaction costs. The portfolio consists of a risk-free asset, and a risky asset whose price is modeled as a geometric Brownian motion....

We analyze the optimal portfolio policy for a multiperiod mean-variance investor facing a large number of risky assets in the presence of general transaction cost. For proportional transaction costs, we give a closed-form expression for a no-trade region, shaped as a multi-dimensional...

We study the impact of parameter uncertainty on the expected utility of a multiperiod investor subject to quadratic transaction costs. We characterize the utility loss associated with ignoring parameter uncertainty, and show that it is equal to the product between the single-period utility loss...