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...

A numerical technique based on the embedding technique proposed in [21, 33] for dynamic mean-variance (MV) optimization problems may yield spurious points, i.e. points which are not on the efficient frontier. In [27], it is shown that spurious points can be eliminated by examining the left upper...

We develop scenario-based stochastic programming models for hedging the risks of international portfolios using options. The models provide an increasing level of integration in managing market and foreign exchange (FX) risks. We start with a single-stage model with currency options for...

We generalize the idea of semi-self-financing strategies, originally discussed in Ehrbar, Journal of Economic Theory (1990), and later formalized in em Cui et al, Mathematical Finance 22 (2012), for the pre-commitment mean-variance (MV) optimal portfolio allocation problem. The proposed...

The present article studies geometric step options in exponential Lévy markets. Our contribution is manifold and extends several aspects of the geometric step option pricing literature. First, we provide symmetry and parity relations and derive various characterizations for both European-type...

The investment industry lacks an unified framework for handling derivative instruments in general portfolio management. With the increased use of derivatives, there is a need for a framework that aligns fundamental terminology and concepts. The main challenges with the current practices are...

We propose a consistent and computationally efficient 2-step methodology for the estimation of multidimensional non-Gaussian asset models built using Lévy processes. The proposed framework allows for dependence between assets and different tail-behaviors and jump structures for each asset. Our...

In Liability Driven Investing (LDI) the profile of future liabilities is an explicit component of the asset allocation process. Similarly, Assets and Liabilities Management (ALM) deals with mismatches between assets and liabilities in banking books. Since extreme events have become the rule in...

We extend the framework of trading strategies of Gatheral [2010] from single stocks to a pair of stocks. Our trading strategy with the executions of two round-trip trades can be described by the trading rates of the paired stocks and the ratio of their trading periods. By minimizing the...

In the present paper we fill an essential gap in the Convertible Bonds pricing world by deriving a Binary Tree based model for valuation subject to credit risk. This model belongs to the framework known as Equity to Credit Risk. We show that this model converges in continuous time to the model...