On the Structure of General Mean-Variance Hedging Strategies

We provide a new characterization of mean-variance hedging strategies in a general semimartingale market. The key point is the introduction of a new probability measure $P^{\star}$ which turns the dynamic asset allocation problem into a myopic one. The minimal martingale measure relative to $P^{\star}$ coincides with the variance-optimal martingale measure relative to the original probability measure $P$.Comment: Published at http://dx.doi.org/10.1214/009117906000000872 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

The law of one price in mean-variance hedging

The law of one price (LOP) broadly asserts that identical financial flows should command the same price. This paper uncovers a new mechanism through which LOP can fail in a continuous-time $L^2(P)$ setting without frictions, namely `trading from just before a predictable stopping time', which surprisingly identifies LOP violations even for continuous price processes. Closing this loophole allows to give a version of the ``Fundamental Theorem of Asset Pricing'' appropriate in the quadratic context, establishing the equivalence of the economic concept of LOP with the probabilistic property of the existence of a local $\mathscr{E}$-martingale state price density. The latter provides unique prices for all square-integrable contingent claims in an extended market and subsequently plays an important role in mean-variance hedging

Simplified calculus for semimartingales: Multiplicative compensators and changes of measure

The paper develops multiplicative compensation for complex-valued semimartingales and studies some of its consequences. It is shown that the stochastic exponential of any complex-valued semimartingale with independent increments becomes a true martingale after multiplicative compensation, where such compensation is meaningful. This generalization of the L\'evy-Khintchin formula fills an existing gap in the literature. We further report Girsanov-type results based on non-negative multiplicatively compensated semimartingales. In particular, we obtain a simplified expression for the multiplicative compensator under the new measure.Comment: 20 pages; new Example 4.

Land-Use Study of the Locality „Na loukách“ in Sudice

Import 27/01/2012Tato diplomová práce řeší návrh zástavby rodinnými domy v lokalitě Na loukách v obci Sudice. Návrh je zpracován ve dvou variantách, přičemž jedna byla vybrána jako prioritní.This master study resolves the suggestions made for building family homes in the locality of „Na Loukách“ in Sudice. The suggested solution was prepared in two variations, one of which was chosen as a priority.Prezenční222 - Katedra městského inženýrstvívelmi dobř

A unified approach to radial, hyperbolic, and directional distance models in Data Envelopment Analysis

The paper analyzes properties of a large class of "path-based" Data Envelopment Analysis models through a unifying general scheme, which includes as standard the well-known oriented radial models, the hyperbolic distance measure model, and the directional distance measure models. The scheme also accommodates variants of standard models over negative data. Path-based models are analyzed from the point of view of nine desired properties that a well-designed model should satisfy. The paper develops mathematical tools that allow systematic investigation of these properties in the general scheme including, but not limited to, the standard path-based models. Among other results, the analysis confirms the generally accepted view that path-based models need not generate Pareto--Koopmans efficient projections, one-to-one identification, or strict monotonicity

Characterization of the Oblique Projector U(VU)+VU(VU)^+V with Application to Constrained Least Squares

We provide a full characterization of the oblique projector $U(VU)^+V$ in the general case where the range of $U$ and the null space of $V$ are not complementary subspaces. We discuss the new result in the context of constrained least squares minimization.Comment: v1: 6 pages v2: 7 pages. Minor changes (formatting, references) in sections 1-2. Extra statement in Theorem 3.1. Substantial revision of section 4 v3: 7 pages. A minor change (more explicit formula for \Xi) in Corollary 4.2. Changed + to direct sum at the bottom of p.5 v4: 7 pages. Removed typo in eq. (17) which was present in v2 and v

Mean-Variance hedging and optimal investment in Heston's model with correlation

This paper solves the mean{variance hedging problem in Heston's model with a stochastic opportunity set moving systematically with the volatility of stock returns. We allow for correlation between stock returns and their volatility (so-called leverage effect). Our contribution is threefold: using a new concept of opportunity-neutral measure we present a simplified strategy for computing a candidate solution in the correlated case. We then go on to show that this candidate generates the true variance-optimal martingale measure; this step seems to be partially missing in the literature. Finally, we derive formulas for the hedging strategy and the hedging error

A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics

We consider the ordinary differential equation x2u′′=axu′+bu−c(u′−1)2,x∈(0,x0), with a∈R,b∈R , c>0 and the singular initial condition u(0)=0, which in financial economics describes optimal disposal of an asset in a market with liquidity effects. It is shown in the paper that if a+b0 then there are infinitely many continuous solutions with indistinguishable asymptotics near 0. Moreover, it is proved that in the latter case there is precisely one solution u corresponding to the choice x 0=∞ which is such that 0≤u(x)≤x for all x>0, and that this solution is strictly increasing and concave

Evaluation of an electro-pneumatic device for artificial capillary pulse generation used in a prospective study in animals for surgical neck wound healing

The paper examines the development and testing of an electro-pneumatic device for wound healing therapy after surgery in the neck area. The device generates air pressure values in a miniaturized cuff using electronic circuitry to drive an electro-valve and air compressor. The device works in two distinct modes: continuous pressure mode and pulsating pressure mode. The pressure value setting can vary from 3 to 11 mmHg, and the pulsating pressure mode's operating frequency range is approximately 0.1 to 0.3 Hz. Laboratory measurements were conducted to evaluate the device's correct functioning in both continuous and pulsating pressure modes. A four-day prospective study with animals (n = 10) was also conducted to evaluate neck wound healing therapy using the electro-pneumatic device. Out of the twelve histological parameters analysed to reveal the differences between the experimental and control wounds, only one demonstrated a significant difference. Out of the ten animals treated with the device, three showed a significant difference in terms of benefit after therapy. We can therefore conclude that the device potentially improves the wound healing process in the neck area if the pre-set air pressure value does not exceed 8 mmHg.Web of Science9art. no. 983