Optimal Transport and Skorokhod Embedding

The Skorokhod embedding problem is to represent a given probability as the distribution of Brownian motion at a chosen stopping time. Over the last 50 years this has become one of the important classical problems in probability theory and a number of authors have constructed solutions with particular optimality properties. These constructions employ a variety of techniques ranging from excursion theory to potential and PDE theory and have been used in many different branches of pure and applied probability. We develop a new approach to Skorokhod embedding based on ideas and concepts from optimal mass transport. In analogy to the celebrated article of Gangbo and McCann on the geometry of optimal transport, we establish a geometric characterization of Skorokhod embeddings with desired optimality properties. This leads to a systematic method to construct optimal embeddings. It allows us, for the first time, to derive all known optimal Skorokhod embeddings as special cases of one unified construction and leads to a variety of new embeddings. While previous constructions typically used particular properties of Brownian motion, our approach applies to all sufficiently regular Markov processes.Comment: Substantial revision to improve the readability of the pape

Model-independent pricing with insider information: a Skorokhod embedding approach

In this paper, we consider the pricing and hedging of a financial derivative for an insider trader, in a model-independent setting. In particular, we suppose that the insider wants to act in a way which is independent of any modelling assumptions, but that she observes market information in the form of the prices of vanilla call options on the asset. We also assume that both the insider's information, which takes the form of a set of impossible paths, and the payoff of the derivative are time-invariant. This setup allows us to adapt recent work of Beiglboeck, Cox and Huesmann (2016) to prove duality results and a monotonicity principle, which enables us to determine geometric properties of the optimal models. Moreover, we show that this setup is powerful, in that we are able to find analytic and numerical solutions to certain pricing and hedging problems

Pathwise super-replication via Vovk's outer measure

Since Hobson's seminal paper [D. Hobson: Robust hedging of the lookback option. In: Finance Stoch. (1998)] the connection between model-independent pricing and the Skorokhod embedding problem has been a driving force in robust finance. We establish a general pricing-hedging duality for financial derivatives which are susceptible to the Skorokhod approach. Using Vovk's approach to mathematical finance we derive a model-independent super-replication theorem in continuous time, given information on finitely many marginals. Our result covers a broad range of exotic derivatives, including lookback options, discretely monitored Asian options, and options on realized variance.Comment: 18 page

Model-independent pricing with insider information:A Skorokhod embedding approach

In this paper we consider the pricing and hedging of financial derivatives in a model-independent setting, for a trader with additional information, or beliefs, on the evolution of asset prices. In particular, we suppose that the trader wants to act in a way which is independent of any modelling assumptions, but that she observes market information in the form of the prices of vanilla call options on the asset. We also assume that both the payoff of the derivative, and the insider's information or beliefs, which take the form of a set of impossible paths, are time-invariant. In this way we accommodate drawdown constraints, as well as information/beliefs on quadratic variation or on the levels hit by asset prices. Our setup allows us to adapt recent work of [12] to prove duality results and a monotonicity principle. This enables us to determine geometric properties of the optimal models. Moreover, for specific types of information, we provide simple conditions for the existence of consistent models for the informed agent. Finally, we provide an example where our framework allows us to compute the impact of the information on the agent's pricing bounds.</p

Outcomes of Childhood Aggression in Women

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75752/1/j.1749-6632.1996.tb32553.x.pd

Early risk factors for adolescent antisocial behaviour: an Australian longitudinal study

Objective: This investigation utilizes data from an Australian longitudinal study to identify early risk factors for adolescent antisocial behaviour. Method: Analyses are based on data from the Mater University Study of Pregnancy, an on-going longitudinal investigation of women’s and children’s health and development involving over 8000 participants. Five types of risk factors (child characteristics, perinatal factors, maternal/familial characteristics, maternal pre- and post-natal substance use and parenting practices) were included in analyses and were based on maternal reports, child assessments and medical records. Adolescent antisocial behaviour was measured when children were 14 years old, using the delinquency subscale of the Child Behaviour Checklist. Results: Based on a series of logistic regression models, significant risk factors for adolescent antisocial behaviour included children’s prior problem behaviour (i.e. aggression and attention/restlessness problems at age 5 years) and marital instability, which doubled or tripled the odds of antisocial behaviour. Perinatal factors, maternal substance use, and parenting practices were relatively poor predictors of antisocial behaviour. Conclusions: Few studies have assessed early predictors of antisocial behaviour in Australia and the current results can be used to inform prevention programs that target risk factors likely to lead to problem outcomes for Australian youth

Destabilization of dark states and optical spectroscopy in Zeeman-degenerate atomic systems

We present a general discussion of the techniques of destabilizing dark states in laser-driven atoms with either a magnetic field or modulated laser polarization. We show that the photon scattering rate is maximized at a particular evolution rate of the dark state. We also find that the atomic resonance curve is significantly broadened when the evolution rate is far from this optimum value. These results are illustrated with detailed examples of destabilizing dark states in some commonly-trapped ions and supported by insights derived from numerical calculations and simple theoretical models.Comment: 14 pages, 10 figure