The Black-Scholes equation is a partial differential that can model the European call option price problem. This be of order natural numbers or fractional. aim this paper to find solution fractional equation. method used solutions these equations Natural decomposition method. Two numerical examples are presented in paper. results show effective and easy use solve

We study restricted computation models related to the tree evaluation problem. The TEP was introduced in earlier work as a simple candidate for the (very) long term goal of separating L and LogDCFL. The input to the problem is a rooted, balanced binary tree of height h, whose internal nodes are labeled with binary functions on [k] = {1, . . . , k} (each given simply as a list of k2 elements of ...

The objective of this paper is twofold. Firstly, to derive time-fractional evolution equation modeling the No-Arbitrage premium Asian option (with arithmetic and geometric averages ) contingent upon an underlying asset that satisfies fractional stochastic differential equation, in a setting when strike price fixed floating. Secondly, we have computed four versions put-call parities for options,...

We consider the classical Merton problem of finding the optimal consumption rate and the optimal portfolio in a Black-Scholes market driven by fractional Brownian motion B with Hurst parameter H > 1/2. The integrals with respect to B are in the Skorohod sense, not pathwise which is known to lead to arbitrage. We explicitly find the optimal consumption rate and the optimal portfolio in such a ma...

Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model is constructed in terms of a fractional Ornstein Uhlenbeck process to have such correlations. It is shown how the associated implied volatility has a term structure that is a f...

In the early Universe matter was crushed to high densities, in a manner similar to that encountered in gravitational collapse to black holes. String theory suggests that the large entropy of black holes can be understood in terms of fractional branes and antibranes. We assume a similar physics for the matter in the early Universe, taking a toroidal compactification and letting branes wrap aroun...

In the early Universe matter was crushed to high densities, in a manner similar to that encountered in gravitational collapse to black holes. String theory suggests that the large entropy of black holes can be understood in terms of fractional branes and antibranes. We assume a similar physics for the matter in the early Universe, taking a toroidal compactification and letting branes wrap aroun...

To examine the relations between erythrocyte sodium-lithium countertransport and renal proximal tubular sodium handling, we measured countertransport, and then subjected 30 normal and 32 hypertensive subjects, both white and black, to provocative maneuvers of volume expansion and contraction. The fractional excretions of sodium and lithium were measured simultaneously. In agreement with previou...