In memoriam: Marco Avellaneda (1955–2022)

Marco Avellaneda (1955–2022) was a leading figure in the development of mathematical modeling in finance and its dissemination among market practitioners. We provide a sketch of his trajectory and outline some of his main research contributions to mathematical finance.     

A model-free approach to continuous-time finance

We present a pathwise approach to continuous-time finance based on causal functional calculus. Our framework does not rely on any probabilistic concept. We introduce a definition of continuous-time self-financing portfolios, which does not rely on any integration concept and show that the value of a self-financing portfolio belongs to a class of nonanticipative functionals, which are pathwise analogs of martingales. We show that if the set of market scenarios is generic in the sense of being stable under certain operations, such self-financing strategies do not give rise to arbitrage. We then consider the problem of hedging a path-dependent payoff across a generic set of scenarios. Applying the transition principle of Rufus Isaacs in differential games, we obtain a pathwise dynamic programming principle for the superhedging cost. We show that the superhedging cost is characterized as the solution of a path-dependent equation. For the Asian option, we obtain an explicit solution.     

HARI: Characteristics of a new defined lifestyle (DL) retirement planning product

Journal of Financial Services Marketing - Approximately 16% of the world's population lives in countries with some concept of a financial retirement plan. Of the remaining population, many do...