A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a drawdown constraint, as in the original setup of Grossman...

We pursue an inverse approach to utility theory and associated consumption and investment problems. Instead of specifying a utility function and deriving the actions of an agent, we assume that we observe the actions of the agent (i.e. consumption and investment strategies) and ask if it is...

We analyze the performance of robust hedging strategies of digital double barrier options of Cox and Obłój (2011) against that of traditional hedging methods such as delta and delta/vega hedging. Digital double barrier options are financial derivative contracts which pay out a fixed amount on...

A new dynamic criterion for measuring the performance of self-financing investment strategies is introduced. To this aim, a family of stochastic processes defined on [0, ∞) and indexed by a wealth argument is used. Optimality is associated with their martingale property along the optimal...

We present a utility-based methodology for the valuation of early exercise contracts in incomplete markets. Incompleteness stems from nontraded assets on which the contracts are written. This methodology takes into account the individual’s attitude towards risk and yields nonlinear pricing...

The paper offers a new perspective on optimal portfolio choice by investigating how and to what extent knowledge of an investor's desirable initial investment choice can be used to determine his future optimal portfolio allocations. Optimality of investment decisions is built on the so-called...