Pathwise stochastic integrals for model free finance

We present two different approaches to stochastic integration in frictionless model free financial mathematics. The first one is in the spirit of It\^o's integral and based on a certain topology which is induced by the outer measure corresponding to the minimal superhedging price. The second one is based on the controlled rough path integral. We prove that every "typical price path" has a naturally associated It\^o rough path, and justify the application of the controlled rough path integral in finance by showing that it is the limit of non-anticipating Riemann sums, a new result in itself. Compared to the first approach, rough paths have the disadvantage of severely restricting the space of integrands, but the advantage of being a Banach space theory. Both approaches are based entirely on financial arguments and do not require any probabilistic structure.Comment: Published at http://dx.doi.org/10.3150/15-BEJ735 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

\u3ci\u3eDemocracy\u27s Discontent\u3c/i\u3e in a Complex World: Can Avalanches, Sandpiles, and Finches Optimize Michael Sandel\u27s Civic Republican Community?

In Democracy\u27s Discontent: America in Search of a Public Philosophy, Michael Sandel looks about him and finds a vast and complex world governed by impersonal institutions and structures, in which discontented, anxious, and frustrated individuals are losing control over the forces that govern their lives, and in which the moral fabric of community is unraveling. His solution is to revitalize the civic strand of freedom found in republican politics and thus equip individuals to govern themselves. Sandel wonders how civic republicanism can exist in today\u27s world. Historically, republicanism has found a home in small, bounded places, which were largely self-sufficient and inhabited by people whose living conditions, education, and commonality enabled them to deliberate about public concerns. His structural answer is to disperse sovereignty both upwards and downwards of the modem nation state into a multiplicity of political communities and social institutions. His normative answer is to infuse substantive moral discourse back into public political debate

Pathwise no-arbitrage in a class of Delta hedging strategies

We consider a strictly pathwise setting for Delta hedging exotic options, based on F\"ollmer's pathwise It\=o calculus. Price trajectories are $d$-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix. The existence of Delta hedging strategies in this pathwise setting is established via existence results for recursive schemes of parabolic Cauchy problems and via the existence of functional Cauchy problems on path space. Our main results establish the nonexistence of pathwise arbitrage opportunities in classes of strategies containing these Delta hedging strategies and under relatively mild conditions on the local volatility matrix

Public Policies against Global Warming

Judged by the principle of intertemporal Pareto optimality, insecure property rights and the greenhouse effect both imply overly rapid extraction of fossil carbon resources. A gradual expansion of demand-reducing public policies – such as increasing ad-valorem taxes on carbon consumption or increasing subsidies for replacement technologies – may exacerbate the problem as it gives resource owners the incentive to avoid future price reductions by anticipating their sales. Useful policies instead involve sequestration, afforestation, stabilization of property rights and emissions trading. Among the public finance measures, constant unit carbon taxes and source taxes on capital income for resource owners stand out.global warming, carbon taxes, Pareto optimality