A framework for valuing derivative securities

This paper develops a general framework for valuing a wide range of derivative securities. Rather than focusing on the stochastic process of the underlying security and developing an instantaneously-riskless hedge portfolio, we focus on the terminal distribution of the underlying security. This enables the derivative security to be valued as the weighted sum of a number of component pieces. The component pieces are simply the different payoffs that the security generates in different states of the world, and they are weighted by the probability of the particular state of the world occurring. A full set of derivations is provided. To illustrate its use, the valuation framework is applied to plain-vanilla call and put options, as well as a range of derivatives including caps, floors, collars, supershares, and digital options.

Diffusion modeling of percutaneous absorption kinetics: 2. Finite vehicle volume and solvent deposited solids

The diffusion model for percutaneous absorption is developed for the specific case of delivery to the skin being limited by the application of a finite amount of solute. Two cases are considered; in the first, there is an application of a finite donor (vehicle) volume, and in the second, there are solvent-deposited solids and a thin vehicle with a high partition coefficient. In both cases, the potential effect of an interfacial resistance at the stratum corneum surface is also considered. As in the previous paper, which was concerned with the application of a constant donor concentration, clearance limitations due to the viable eqidermis, the in vitro sampling rate, or perfusion rate in vivo are included. Numerical inversion of the Laplace domain solutions was used for simulations of solute flux and cumulative amount absorbed and to model specific examples of percutaneous absorption of solvent-deposited solids. It was concluded that numerical inversions of the Laplace domain solutions for a diffusion model of the percutaneous absorption, using standard scientific software (such as SCIENTIST, MicroMath Scientific software) on modern personal computers, is a practical alternative to computation of infinite series solutions. Limits of the Laplace domain solutions were used to define the moments of the flux-time profiles for finite donor volumes and the slope of the terminal log flux-time profile. The mean transit time could be related to the diffusion time through stratum corneum, viable epidermal, and donor diffusion layer resistances and clearance from the receptor phase. Approximate expressions for the time to reach maximum flux (peak time) and maximum flux were also derived. The model was then validated using reported amount-time and flux-time profiles for finite doses applied to the skin. It was concluded that for very small donor phase volume or for very large stratum corneum-vehicle partitioning coefficients (e.g., for solvent deposited solids), the flux and amount of solute absorbed are affected by receptor conditions to a lesser extent than is obvious for a constant donor constant donor concentrations. (C) 2001 Wiley-Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 90:504-520, 2001.

Identifying trajectories of adolescent smoking: An application of latent growth mixture modeling

The goal of the current study was to identify discrete longitudinal patterns of change in adolescent smoking using latent growth mixture modeling. Five distinct longitudinal patterns were identified. A group of early rapid escalators was characterized by early escalation (at age 13) that rapidly increased to heavy smoking. A pattern characterized by occasional puffing up until age 15, at which time smoking escalated to moderate levels was also identified (late moderate escalators). Another group included adolescents who, after age 15, began to escalate slowly in their smoking to light (0.5 cigarettes per month) levels (late slow escalators). Finally, a group of stable light smokers (those who smoked 1-2 cigarettes per month) and a group of stable puffers (those. who smoked only a few puffs per month) were also identified. The stable puffer group was the largest group and represented 25% of smokers.