Pricing and hedging in incomplete markets with coherent risk

We propose a pricing technique based on coherent risk measures, which enables one to get finer price intervals than in the No Good Deals pricing. The main idea consists in splitting a liability into several parts and selling these parts to different agents. The technique is closely connected with the convolution of coherent risk measures and equilibrium considerations. Furthermore, we propose a way to apply the above technique to the coherent estimation of the Greeks

CAPM, rewards, and empirical asset pricing with coherent risk

The paper has 2 main goals: 1. We propose a variant of the CAPM based on coherent risk. 2. In addition to the real-world measure and the risk-neutral measure, we propose the third one: the extreme measure. The introduction of this measure provides a powerful tool for investigating the relation between the first two measures. In particular, this gives us - a new way of measuring reward; - a new approach to the empirical asset pricing

Coherent measurement of factor risks

We propose a new procedure for the risk measurement of large portfolios. It employs the following objects as the building blocks: - coherent risk measures introduced by Artzner, Delbaen, Eber, and Heath; - factor risk measures introduced in this paper, which assess the risks driven by particular factors like the price of oil, S&P500 index, or the credit spread; - risk contributions and factor risk contributions, which provide a coherent alternative to the sensitivity coefficients. We also propose two particular classes of coherent risk measures called Alpha V@R and Beta V@R, for which all the objects described above admit an extremely simple empirical estimation procedure. This procedure uses no model assumptions on the structure of the price evolution. Moreover, we consider the problem of the risk management on a firm's level. It is shown that if the risk limits are imposed on the risk contributions of the desks to the overall risk of the firm (rather than on their outstanding risks) and the desks are allowed to trade these limits within a firm, then the desks automatically find the globally optimal portfolio

Shape Instabilities in the Dynamics of a Two-component Fluid Membrane

We study the shape dynamics of a two-component fluid membrane, using a dynamical triangulation monte carlo simulation and a Langevin description. Phase separation induces morphology changes depending on the lateral mobility of the lipids. When the mobility is large, the familiar labyrinthine spinodal pattern is linearly unstable to undulation fluctuations and breaks up into buds, which move towards each other and merge. For low mobilities, the membrane responds elastically at short times, preferring to buckle locally, resulting in a crinkled surface.Comment: 4 pages, revtex, 3 eps figure

A Novel Monte Carlo Approach to the Dynamics of Fluids --- Single Particle Diffusion, Correlation Functions and Phase Ordering of Binary Fluids

We propose a new Monte Carlo scheme to study the late-time dynamics of a 2-dim hard sphere fluid, modeled by a tethered network of hard spheres. Fluidity is simulated by breaking and reattaching the flexible tethers. We study the diffusion of a tagged particle, and show that the velocity autocorrelation function has a long-time $t^{-1}$ tail. We investigate the dynamics of phase separation of a binary fluid at late times, and show that the domain size $R(t)$ grows as $t^{1/2}$ for high viscosity fluids with a crossover to $t^{2/3}$ for low viscosity fluids. Our scheme can accomodate particles interacting with a pair potential $V(r)$,and modified to study dynamics of fluids in three dimensions.Comment: Latex, 4 pages, 4 figure

Selfdecomposability of Weak Variance Generalised Gamma Convolutions

Weak variance generalised gamma convolution processes are multivariate Brownian motions weakly subordinated by multivariate Thorin subordinators. Within this class, we extend a result from strong to weak subordination that a driftless Brownian motion gives rise to a self-decomposable process. Under moment conditions on the underlying Thorin measure, we show that this condition is also necessary. We apply our results to some prominent processes such as the weak variance alpha-gamma process, and illustrate the necessity of our moment conditions in some cases

Stochastic Volatility for Levy Processes.

Three processes reflecting persistence of volatility are initially formulated by evaluating three Lévy processes at a time change given by the integral of a mean-reverting square root process. The model for the mean-reverting time change is then generalized to include non-Gaussian models that are solutions to Ornstein-Uhlenbeck equations driven by one-sided discontinuous Lévy processes permitting correlation with the stock. Positive stock price processes are obtained by exponentiating and mean correcting these processes, or alternatively by stochastically exponentiating these processes. The characteristic functions for the log price can be used to yield option prices via the fast Fourier transform. In general mean-corrected exponentiation performs better than employing the stochastic exponential. It is observed that the mean-corrected exponential model is not a martingale in the filtration in which it is originally defined. This leads us to formulate and investigate the important property of martingale marginals where we seek martingales in altered filtrations consistent with the one-dimensional marginal distributions of the level of the process at each future date.Risque de marché; Gestion du risque; Volatilité (finances); Risk management; Volatility (finance); Stochastic processes; Processus stochastiques; Finances; Modèles mathématiques;