This overview article concerns the notion of fractional smoothness of random variables of the form g(XT ), where X = (Xt)t∈[0,T ] is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in stochastic finance mainly concern the analysis of discrete time hedging errors. We close the review by indic...

This overview article concerns the notion of fractional smoothness of random variables of the form g(XT ), where X = (Xt)t∈[0,T ] is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in stochastic finance mainly concern the analysis of discrete time hedging errors. We close the review by indic...

We obtain closed–form expressions for the prices and optimal hedging strategies of American put–options in the presence of an “up–and–out” barrier, both with and without constraints on the short–selling of stock. The constrained case leads to a stochastic optimization problem of mixed optimal stopping/singular control type. This is reduced to a variational inequality which is then solved explic...

This article attempts to extend the complete market option pricing theory to incomplete markets. Instead of eliminating the risk by a perfect hedging portfolio, partial hedging will be adopted and some residual risk at expiration will be tolerated. The risk measure (or risk indifference) prices charged for buying or selling an option are associated to the capital required for dynamic hedging so...

We address the problem of hedging inventory risk for a short lifecycle or seasonal item when its demand is correlated with the price of a financial asset. We show how to construct optimal hedging transactions that minimize the variance of profit and increase the expected utility for a risk-averse decision-maker. We show that for a wide range of hedging strategies and utility functions, a risk-a...

This chapter studies structural and reduced-form credit risk models under incomplete information using techniques from stochastic filtering. We start with a brief introduction to stochastic filtering. Next we cover the pricing of corporate securities (debt and equity) in structural models under partial information. Furthermore we study the construction of a dynamic reduced-form credit risk mode...

This paper examines optimal portfolios with discounted stochastic cash inflows (SCI). The cash inflows are invested into a market that is characterized by inflation-linked bond, a stock and a cash account. It was assumed that inflationlinked bond, stock and the cash inflows are stochastic and follow a standard geometric Brownian motion. The variational form of Merton portfolio strategy was obta...

despite the importance of hedging in academic productions, its use in different disciplines and genres has been given little attention (hyland, 1998; crystal, 1995). more precisely, the role of different genders as contributors to this social phenomenon (i.e., research articles) has been taken as neutral, as if gender is inconsequential in identity construction. the studies done in english sugg...

one tactful strategy in political rhetoric is hedging which is associated with vagueness and innuendos. despite the studies that address hedging in academic discourse and conversation analysis, studies that investigate hedges in relation to political power, face, and politeness are tremendously few. to this aim, four political interviews were selected from cnn and bbc websites on the basis of t...