Option Pricing with Delayed Information

We propose a model to study the effects of delayed information on option pricing. We first talk about the absence of arbitrage in our model, and then discuss super replication with delayed information in a binomial model, notably, we present a closed form formula for the price of convex contingent claims. Also, we address the convergence problem as the time-step and delay length tend to zero and introduce analogous results in the continuous time framework. Finally, we explore how delayed information exaggerates the volatility smile

Pathogenesis of AD is similar to that of uremic encephalopathy of Homocysteic acid.

Homocysteic acid (HA) has been established as a pathogen in Alzheimer's disease (AD) in 3xTg-AD model mice. However, it is not established whether HA is involved in the AD pathogenesis in humans. We investigated the relationship between urinary HA levels and Mini-Mental State Examination (MMSE) scores in patients with AD (n = 110, normal =22, AD=88) and found a positive, statistically significant relationship between the two variables (r = 0.39, p =0.00003, n = 110). This relationship was stronger in females. (r = 0.47, p = 0.00008, n = 65 in females; r = 0.39, p = 0.02, n =45 in males). The difference in the urinary HA level between normal and AD females was statistically significant (normal:18.4 + 10.6vsAD: 9.1 + 7.2 mM,p<0.01), but this difference in males was not statistically significant. (normal:12.7 + 6 vs AD8.8 + 7.8). Smoking, hypertension, and diabetes mellitus decreased urinary HA excretion. On the basis of these results, we showed that HA is usually excreted into urine in humans and did not affect brain function in normal individuals. However, when urinary HA excretion was decreased, HA was shown to damage brain function, particularly cognitive ability. To confirm our hypothesis, that is, when urinary HA is suppressed to be excreted into urine, the blood HA level will increase, we examined the relationship between the urinary HA level and blood HA level in 19 patients. The result was shown that the negative statistically significant relationship between them was observed (r=-0.6, p=0.007, n=19). From this result, the uremic encephalopathy of HA toxicity was confirmed. However there remains the question of how the blood HA affected the brain's cognitive function. The direct effect of green tea leaves ingestion on HA level and MMSE score were also observed. Ingested green tea leaves decreased HA level in blood and concomitantly increased MMSE score, suggesting that blood HA could affect cognitive function. But How? Some papers showed that exogenous NMDA including HA disrupted the blood brain barrier and entered into the brain and affected the cognitive function to decrease MMSE score. These results indicate that human AD pathogenesis is influenced by HA, and that HA is a human pathogen in AD, indicating that the pathogenesis of AD is similar to that of uremic encephalopathy. Also, urinary HA can be used as a biomarker for Alzheimer's disease

Efficient estimation of one-dimensional diffusion first passage time densities via Monte Carlo simulation

We propose a method for estimating first passage time densities of one-dimensional diffusions via Monte Carlo simulation. Our approach involves a representation of the first passage time density as expectation of a functional of the three-dimensional Brownian bridge. As the latter process can be simulated exactly, our method leads to almost unbiased estimators. Furthermore, since the density is estimated directly, a convergence of order $1 / \sqrt{N}$, where $N$ is the sample size, is achieved, the last being in sharp contrast to the slower non-parametric rates achieved by kernel smoothing of cumulative distribution functions.Comment: 14 pages, 2 figure

Hybrid Atlas models

We study Atlas-type models of equity markets with local characteristics that depend on both name and rank, and in ways that induce a stable capital distribution. Ergodic properties and rankings of processes are examined with reference to the theory of reflected Brownian motions in polyhedral domains. In the context of such models we discuss properties of various investment strategies, including the so-called growth-optimal and universal portfolios.Comment: Published in at http://dx.doi.org/10.1214/10-AAP706 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org