Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Monte Carlo Study of the Growth of L12 ordered domains in fcc A3B binary alloys

A Monte Carlo study of the late time growth of L12-ordered domains in a fcc A3B binary alloy is presented. The energy of the alloy has been modeled by a nearest-neighbor interaction Ising Hamiltonian. The system exhibits a fourfold degenerated ground state and two kinds of interfaces separating ordered domains: flat and curved antiphase boundaries. Two different dynamics are used in the simulations: the standard atom-atom exchange mechanism and the more realistic vacancy-atom exchange mechanism. The results obtained by both methods are compared. In particular we study the time evolution of the excess energy, the structure factor and the mean distance between walls. In the case of atom-atom exchange mechanism anisotropic growth has been found: two characteristic lengths are needed in order to describe the evolution. Contrarily, with the vacancyatom exchange mechanism scaling with a single length holds. Results are contrasted with existing experiments in Cu3Au and theories for anisotropic growth.

Magnetic phase separation in ordered alloys

We present a lattice model to study the equilibrium phase diagram of ordered alloys with one magnetic component that exhibits a low temperature phase separation between paramagnetic and ferromagnetic phases. The model is constructed from the experimental facts observed in Cu3-xAlMnx and it includes coupling between configurational and magnetic degrees of freedom that are appropriate for reproducing the low temperature miscibility gap. The essential ingredient for the occurrence of such a coexistence region is the development of ferromagnetic order induced by the long-range atomic order of the magnetic component. A comparative study of both mean-field and Monte Carlo solutions is presented. Moreover, the model may enable the study of the structure of ferromagnetic domains embedded in the nonmagnetic matrix. This is relevant in relation to phenomena such as magnetoresistance and paramagnetism

Ordered structures in rotating ultracold Bose gases

Two-dimentional systems of trapped samples of few cold bosonic atoms submitted to strong rotation around the perpendicular axis may be realized in optical lattices and microtraps. We investigate theoretically the evolution of ground state structures of such systems as the rotational frequency Omega increases. Various kinds of ordered structures are observed. In some cases, hidden interference patterns exhibit themselves only in the pair correlation function; in some other cases explicit broken-symmetry structures appear that modulate the density. For N < 10 atoms, the standard scenario, valid for large sytems is absent, and is only gradually recovered as N increases. On the one hand, the Laughlin state in the strong rotational regime contains ordered structures much more similar to a Wigner molecule than to a fermionic quantum liquid. On the other hand, in the weak rotational regime, the possibility to obtain equilibrium states, whose density reveals an array of vortices, is restricted to the vicinity of some critical values of the rotational frequency Omega.

Long-range-interactions induced ordered structures in deposition processes

We present a new model of sequential adsorption in which the adsorbing particles experience dipolar interactions. We show that in the presence of these long-range interactions, highly ordered structures in the adsorbed layer may be induced at low temperatures. The new phenomenology is manifest through significant variations of the pair correlation function and the jamming limit, with respect to the case of noninteracting particles. Our study could be relevant in understanding the adsorption of magnetic colloidal particles in the presence of a magnetic field.

Blood lymphocyte subsets in rats with adjuvant arthritis

To determine the phenotype of peripheral blood lymphocytes during the time-course of adjuvant arthritis (AA) to detect alterations that could be involved in the pathogenesis of the arthritic process. METHODS--Phenotype analysis was performed on days 7, 14, 21, 28, 42, 56 and 70 after arthritis induction using monoclonal antibodies to CD5, CD4 and CD8 subsets, and flow cytometry. The proportion of activated lymphocytes and lymphocytes was also assessed with monoclonal antibodies to IL-2R (CD25), to Ia antigen and by polyclonal antibodies to rat Ig. RESULTS--Adjuvant arthritis produced leukocytosis with neutrophilia. Rats with AA showed a marked increase in the number of both CD4+ and CD8+ cells. The ratio CD4/CD8 decreased because the rise in CD8+ cells was more pronounced than the increase in CD4+ cells. Changes in lymphocyte counts showed two well-defined periods: the first, from day 14 to day 28, during which the inflammation of the joints reached a maximum and changes in lymphocyte subsets were more pronounced, that is, there was a threefold increase in CD8+ lymphocytes over normal counts, and the second, from day 42 to day 70, in which modified parameters improved considerably but remained different from controls. CONCLUSION--Alterations were detected in the phenotype of peripheral blood lymphocytes in AA, which provides an additional marker of disease activity.

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Peripheral T cell activation and deletion induced by transfer of lymphocyte subsets expressing endogenous or exogenous mouse mammary tumor virus.

Murine T cell reactivity with products of the minor lymphocyte stimulatory (Mls) locus correlates with the expression of particular variable (V) domains of the T cell receptor (TCR) beta chain. It was recently demonstrated that Mls antigens are encoded by an open reading frame (ORF) in the 3' long terminal repeat of either endogenous or exogenous mouse mammary tumor virus (MMTV). Immature thymocytes expressing reactive TCR-V beta domains are clonally deleted upon exposure to endogenous Mtv's. Mature T cells proliferate vigorously in response to Mls-1a (Mtv-7) in vivo, but induction of specific anergy and deletion after exposure to Mtv-7-expressing cells in the periphery has also been described. We show here that B cells and CD8+ (but not CD4+) T cells from Mtv-7+ mice efficiently induce peripheral deletion of reactive T cells upon transfer to Mtv-7- recipients, whereas only B cells stimulate specific T cell proliferation in vivo. In contrast to endogenous Mtv-7, transfer of B, CD4+, or CD8+ lymphocyte subsets from mice maternally infected with MMTV(SW), an infectious homologue of Mtv-7, results in specific T cell deletion in the absence of a detectable proliferative response. Finally, we show by secondary transfers of infected cells that exogenous MMTV(SW) is transmitted multidirectionally between lymphocyte subsets and ultimately to the mammary gland. Collectively our data demonstrate heterogeneity in the expression and/or presentation of endogenous and exogenous MMTV ORF by lymphocyte subsets and emphasize the low threshold required for induction of peripheral T cell deletion by these gene products.

Differential role of naïve and memory CD4 T-cell subsets in primary alloresponses.

The T cell response to major histocompatibility complex (MHC) alloantigens occurs via two main pathways. The direct pathway involves the recognition of intact allogeneic MHC:peptide complexes on donor cells and provokes uniquely high frequencies of responsive T cells. The indirect response results from alloantigens being processed like any other protein antigen and presented as peptide by autologous antigen-presenting cells. The frequencies of T cells with indirect allospecificity are orders of magnitude lower and comparable to other peptide-specific responses. In this study, we explored the contributions of naïve and memory CD4(+) T cells to these two pathways. Using an adoptive transfer and skin transplantation model we found that naive and memory CD4(+) T cells, both naturally occurring and induced by sensitization with multiple third-party alloantigens, contributed equally to graft rejection when only the direct pathway was operative. In contrast, the indirect response was predominantly mediated by the naïve subset. Elimination of regulatory CD4(+)CD25(+) T cells enabled memory cells to reject grafts through the indirect pathway, but at a much slower tempo than for naïve cells. These findings have implications for better targeting of immunosuppression to inhibit immediate and later forms of alloimmunity.

Differentiation associated regulation of microRNA expression in vivo in human CD8+ T cell subsets.

BACKGROUND: The differentiation of CD8+ T lymphocytes following priming of naïve cells is central in the establishment of the adaptive immune response. Yet, the molecular events underlying this process are not fully understood. MicroRNAs have been recently shown to play a key role in the regulation of haematopoiesis in mouse, but their implication in peripheral lymphocyte differentiation in humans remains largely unknown. METHODS: In order to explore the potential implication of microRNAs in CD8+ T cell differentiation in humans, microRNA expression profiles were analysed using microarrays and quantitative PCR in several human CD8+ T cell subsets defining the major steps of the T cell differentiation pathway. RESULTS: We found expression of a limited set of microRNAs, including the miR-17~92 cluster. Moreover, we reveal the existence of differentiation-associated regulation of specific microRNAs. When compared to naive cells, miR-21 and miR-155 were indeed found upregulated upon differentiation to effector cells, while expression of the miR-17~92 cluster tended to concomitantly decrease. CONCLUSIONS: This study establishes for the first time in a large panel of individuals the existence of differentiation associated regulation of microRNA expression in human CD8+ T lymphocytes in vivo, which is likely to impact on specific cellular functions.

Sensitive gene expression profiling of human T cell subsets reveals parallel post-thymic differentiation for CD4+ and CD8+ lineages.

The differentiation of CD4(+) or CD8(+) T cells following priming of naive cells is central in the establishment of the immune response against pathogens or tumors. However, our understanding of this complex process and the significance of the multiple subsets of differentiation remains controversial. Gene expression profiling has opened new directions of investigation in immunobiology. Nonetheless, the need for substantial amount of biological material often limits its application range. In this study, we have developed procedures to perform microarray analysis on amplified cDNA from low numbers of cells, including primary T lymphocytes, and applied this technology to the study of CD4 and CD8 lineage differentiation. Gene expression profiling was performed on samples of 1000 cells from 10 different subpopulations, defining the major stages of post-thymic CD4(+) or CD8(+) T cell differentiation. Surprisingly, our data revealed that while CD4(+) and CD8(+) T cell gene expression programs diverge at early stages of differentiation, they become increasingly similar as cells reach a late differentiation stage. This suggests that functional heterogeneity between Ag experienced CD4(+) and CD8(+) T cells is more likely to be located early during post-thymic differentiation, and that late stages of differentiation may represent a common end in the development of T-lymphocytes.

Inequality measurement for ordered response health data

When health status is an ordered response variable, Allison and Foster (2004)postulate that a distribution Q exhibits more inequality than a distribution P if Q is obtained from P via a sequence of median preserving spreads. This paper introduces a parametric family of inequality indices which are founded on the Allison and Foster ordering. [Authors]

Expectation to improve cardiovascular risk factors control in participants to a health promotion program.

BACKGROUND: We assessed expectations to improve cardiovascular disease risk factors (CVD-RF) in participants to a health promotion program. PARTICIPANTS AND METHODS: Blood pressure (BP), blood glucose (BG), blood total cholesterol (TC), body mass index (BMI), and self-reported smoking were assessed in 1,598 volunteers from the general public (men: 40%; mean age: 56.7 +/- 12.7 years) participating in a mobile health promotion program in the Vaud canton, Switzerland. Participants were asked about their expectation to have their CVD-RF improved at a next visit scheduled 2-3 years later. RESULTS: Expectation for improved control was found in 90% of participants with elevated BP, 91% with elevated BG, 45% with elevated TC, 44% who were overweight, and 35% who were smoking. Expectation for TC improvement was reported more often by men, persons with high level of TC, and persons who had consulted a doctor in the past 12 months. Expectations to lose weight and to quit smoking were found more often in younger persons than the older ones. CONCLUSION: Volunteers from the general population participating in a health promotion program expected improved control more often for hypertension and dysglycemia than for dyslipidemia, overweight and smoking.