Extended weak convergence and utility maximisation with proportional transaction costs

Finance and Stochastics - In this paper, we study utility maximisation with proportional transaction costs. Assuming extended weak convergence of the underlying processes, we prove the convergence...     

LIMIT THEOREMS FOR PARTIAL HEDGING UNDER TRANSACTION COSTS

We study shortfall risk minimization for American options with path‐dependent payoffs under proportional transaction costs in the Black–Scholes (BS) model. We show that for this case the shortfall risk is a limit of similar terms in an appropriate sequence of binomial models. We also prove that in the continuous time BS model, for a given initial capital, there exists a portfolio strategy which minimizes the shortfall risk. In the absence of transactions costs (complete markets) similar limit theorems were obtained by Dolinsky and Kifer for game options. In the presence of transaction costs the markets are no longer complete and additional machinery is required. Shortfall risk minimization for American options under transaction costs was not studied before.     

Duality and convergence for binomial markets with friction

We prove limit theorems for the super-replication cost of European options in a binomial model with friction. Examples covered are markets with proportional transaction costs and illiquid markets. A dual representation for the super-replication cost in these models is obtained and used to prove the limit theorems. In particular, the existence of a liquidity premium for the continuous-time limit of the model proposed in Çetin et al. (Finance Stoch. 8:311–341, 2004) is proved. Hence, this paper extends the previous convergence result of Gökay and Soner (Math Finance 22:250–276, 2012) to the general non-Markovian case. Moreover, the special case of small transaction costs yields, in the continuous limit, the G-expectation of Peng as earlier proved by Kusuoka (Ann. Appl. Probab. 5:198–221, 1995).     

Robust hedging with proportional transaction costs

A 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. The investor’s portfolio consists of a dynamically traded stock and a static position in vanilla options, which can be exercised at maturity. Trading of both options and stock is subject to proportional transaction costs. The main theorem is a duality between hedging and a Monge–Kantorovich-type optimization problem. In this dual transport problem, the optimization is over all probability measures that satisfy an approximate martingale condition related to consistent price systems, in addition to an approximate marginal constraint.     

PERFECT AND PARTIAL HEDGING FOR SWING GAME OPTIONS IN DISCRETE TIME

The paper introduces and studies hedging for game (Israeli) style extension of swing options considered as multiple exercise derivatives. Assuming that the underlying security can be traded without restrictions, we derive a formula for valuation of multiple exercise options via classical hedging arguments. Introducing the notion of the shortfall risk for such options we study also partial hedging which leads to minimization of this risk.     

Linguistic barriers to consumer information processing: Information overload in the hispanic population

The ability of individuals to assimilate and process consumer information appears to have finite limits. If consumers are given information which exceeds their processing capacity, information overload is said to exist and results in less effective decision making. The relationship between information overload and linguistic ability was investigated in this study. Americans and Hispanics were presented with varying amounts of consumer information in their native and non-native language. As predicted, information can act as a stressor, affecting decision making in a non-native language prior to affecting decision making in a dominant language. Information overload occurred sooner in Hispanics and Americans when consumer information was presented in their non-dominant language.     

Super‐replication in fully incomplete markets

In this work, we introduce the notion of fully incomplete markets. We prove that for these markets, the super‐replication price coincides with the model‐free super‐replication price. Namely, the knowledge of the model does not reduce the super‐replication price. We provide two families of fully incomplete models: stochastic volatility models and rough volatility models. Moreover, we give several computational examples. Our approach is purely probabilistic.     

A scaling limit for utility indifference prices in the discretised Bachelier model

Finance and Stochastics - We consider the discretised Bachelier model where hedging is done on a set of equidistant times. Exponential utility indifference prices are studied for path-dependent...     

Health and Female Self-Employment

This study uses data from the Mature Women's Cohort of the National Longitudinal Survey of Labor Market Experience (NLSLME). The sample (n = 1,412) comprises self-employed, wage-earning, and nonemployed women whose cumulative employment is measured by employment status between 1976 and 1995 and whose health status was measured in 1976 and in 1995. Three multivariate regression models, one for each type of employment status, are used to control for sociodemographic and for other factors thought to influence health status in 1995, including health status in 1976. The study finds that unemployment resulted in a significantly negative health status in 1995 compared to women of similar age, while the effect of working for wages results in significantly positive health relative to women of similar age. Self-employment had no statistically significant effect on health status in 1995, thus indicating that the health of the self-employed, while better than that of the nonemployed, substantially was worse than that of wage earners.     

The scaling limit of superreplication prices with small transaction costs in the multivariate case

Kusuoka (Ann. Appl. Probab. 5:198–221, 1995) showed how to obtain non-trivial scaling limits of superreplication prices in discrete-time models of a single risky asset which is traded at properly scaled proportional transaction costs. This article extends the result to a multivariate setup where the investor can trade in several risky assets. The \(G\)-expectation describing the limiting price involves models with a volatility range around the frictionless scaling limit that depends not only on the transaction costs coefficients, but also on the chosen complete discrete-time reference model.