We develop a class of pathwise inequalities of the form $H(B_t)\ge M_t+F(L_t)$, where $B_t$ is Brownian motion, $L_t$ its local time at zero and $M_t$ a local martingale. The concrete nature of the representation makes the inequality useful for a variety of applications. In this work, we use the...

In this article we are interested in option pricing in markets with bubbles. A bubble is defined to be a price process which, when discounted, is a local martingale under the risk-neutral measure but not a martingale. We give examples of bubbles both where volatility increases with the price...

This paper studies a variant of the contest model introduced by Seel and Strack. In the Seel-Strack contest, each agent or contestant privately observes a Brownian motion, absorbed at zero, and chooses when to stop it. The winner of the contest is the contestant who stops at the highest value....

This paper discusses the gambling contest introduced in Seel & Strack (Gambling in contests, Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 375, Mar 2012.) and considers the impact of adding a penalty associated with failure to follow a winning strategy....

A variance swap is a derivative with a path-dependent payoff which allows investors to take positions on the future variability of an asset. In the idealised setting of a continuously monitored variance swap written on an asset with continuous paths it is well known that the variance swap payoff...

We pursue an inverse approach to utility theory and consumption & investment problems. Instead of specifying an agent's utility function and deriving her actions, we assume we observe her actions (i.e. her consumption and investment strategies) and ask if it is possible to derive a utility...

<Para ID="Par1">We consider the problem of giving a robust, model-independent, lower bound on the price of a forward starting straddle with payoff <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$|F_{T_{1}} - F_{T_{0}}|$</EquationSource> </InlineEquation>, where 0T <Subscript>0</Subscript>T <Subscript>1</Subscript>. Rather than assuming a model for the underlying forward price (F <Subscript> t </Subscript>)<Subscript> t≥0</Subscript>, we assume that call prices for maturities T...</subscript></subscript></subscript></subscript></subscript></equationsource></inlineequation></para>