We construct portfolios with an alternative selection criterion, the Omega function, which can be expressed as the ratio of two partial moments of the returns distribution. Finding Omega-optimal portfolios, in particular under realistic constraints like cardinality restrictions, requires to...

In modern portfolio theory, financial portfolios are characterised by a desired property, the 'reward', and something undesirable, the 'risk'. While these properties are commonly identified with mean and variance of returns, respectively, we test alternative specifications like partial and...

Hedge funds offer desirable risk-return profiles; but we also find high management fees, lack of transparency and worse, very limited liquidity (they are often closed to new investors and disinvestment fees can be prohibitive). This creates an incentive to replicate the attractive features of...

An investor with constant relative risk aversion trades a safe and several risky assets with constant investment opportunities. For a small fixed transaction cost, levied on each trade regardless of its size, we explicitly determine the leading-order corrections to the frictionless value...

We consider a stochastic optimization problem of maximizing the expected utility from terminal wealth in an illiquid market. A discrete time model is constructed with few additional state variables. The dynamic programming approach is then developed and used for numerical studies. No-arbitrage...

Duality for robust hedging with proportional transaction costs of path dependent European options is obtained in a discrete time financial market with one risky asset. Investor's portfolio consists of a dynamically traded stock and a static position in vanilla options which can be exercised at...

We consider the classical Merton problem of lifetime consumption-portfolio optimization problem with small proportional transaction costs. The first order term in the asymptotic expansion is explicitly calculated through a singular ergodic control problem which can be solved in closed form in...

We establish the existence and characterization of a primal and a dual facelift - discontinuity of the value function at the terminal time - for utility maximization in incomplete semimartingale-driven financial markets. Unlike in the lower- and upper-hedging problems, and somewhat unexpectedly,...

We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small transaction costs is used to obtain a tractable model. A...