A number of variants of the classical Markowitz mean-variance optimization model for portfolio selection have been investigated to render it more realistic. Recently, it has been studied the imposition of a cardinality constraint, setting an upper bound on the number of active positions taken in the portfolio, in an attempt to improve its performance and reduce transactions costs. However, one ...

where t runs from 0 onwards, the supremum is taken over stopping times τ of X , and c > 0 is a given and fixed constant. Using direct martingale arguments we first show that when μ ≤ 0 it is optimal to stop at once and when μ ≥ σ/2 it is optimal not to stop at all. By employing the method of Lagrange multipliers we then show that the nonlinear problem for 0 < μ < σ/2 can be reduced to a family ...

We consider the Generalised Normal Variance-Mean (GNVM) model in which the mixing random variable is Gamma distributed for financial return data. This model generalises the popular Variance-Gamma (VG) distribution. This GNVM model can be interpreted as the addition of noise to a (skew) VG base. In this presentation, we will not only discuss the parameter estimation of the general model, but als...

Electronic trading of equities and other securities makes heavy use of “arrival price” algorithms, that balance the market impact cost of rapid execution against the volatility risk of slow execution. In the standard formulation, mean-variance optimal trading strategies are static: they do not modify the execution speed in response to price motions observed during trading. We show that substant...

The Mean-Variance Portfolio Theory continues to be the cardinal tool for much of portfolio management. Traditional concerted literature on the Mean-Variance theory can be segmented almost exclusively into (i) chapters in books that provide simply a write up on the theory and (ii) books that contain a purely mathematical analysis without emphasizing the financial implications and interpretations...

In this article we discuss the multilevel Monte Carlo method for stochastic differential equations driven by jump-diffusion processes. We show that for a reasonable jump intensity the multilevel Monte Carlo method for jump-diffusions reduces the computational complexity compared to the standard Monte Carlo method significantly for a given mean square accuracy. Carrying out numerical experiments...