About discrete hedging and option pricing

The approach that allows find European option price on the assumption of hedging at discrete times is proposed. The routine allows find the option price not for lognormal distribution functions of underlying asset only but for other classes of distribution functions too. It is shown that there exists a nonzero possibility that market parameters can take values such that to realize the hedging policy becomes impossible. This fact is not in contradiction with Black-Scholes option price model as long as this possibility tends to zero at the limit of continuous hedging.option pricing model, finance mathematical model, discrete hedging

Reality of Manned Flying Reactor

New concept for reducing dose radiation exposure, which helps to decrease the duration and cost of deep space human missions is introduced. This concept can be efficiently realized, using modern materials, such as carbon nanotube composites.Comment: 3 pages, 1 figure; minor change

On asymptotic value for dynamic games with saddle point

The paper is concerned with two-person games with saddle point. We investigate the limits of value functions for long-time-average payoff, discounted average payoff, and the payoff that follows a probability density. Most of our assumptions restrict the dynamics of games. In particular, we assume the closedness of strategies under concatenation. It is also necessary for the value function to satisfy Bellman's optimality principle, even if in a weakened, asymptotic sense. We provide two results. The first one is a uniform Tauber result for games: if the value functions for long-time-average payoff converge uniformly, then there exists the uniform limit for probability densities from a sufficiently broad set; moreover, these limits coincide. The second one is the uniform Abel result: if a uniform limit for self-similar densities exists, then the uniform limit for long-time average payoff also exists, and they coincide.Comment: for SIAM CT1