This article develops an option pricing model to evaluate knowledge management (KM) activities from the following perspectives: knowledge creation, knowledge conversion, knowledge circulation, and knowledge carry out. This paper makes three important contributions: (1) it provides a formal theoretical grounding for the validity of the Black-Scholes model that might be employed to KM; (2) it pro...

denote an increment of the BM (with ds > 0). We also use N(μ, σ2) to denote a normal distribution with mean μ and variance σ2. Recall some of the key properties of BM: (i) B0 = 0; (ii) independent increments, i.e., dBs and dBt are independent, for any s + ds ≤ t; (iii) stationary increments, i.e., dBs follows a normal distribution N(0, ds). Note this last distribution depends only on the length...

In this paper, Laplace homotopy perturbation method, which is combined form of the Laplace transform and the homotopy perturbation method, is employed to obtain a quick and accurate solution to the fractional Black Scholes equation with boundary condition for a European option pricing problem. The Black-Scholes formula is used as a model for valuing European or American call and put options on ...

We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a Hamilton-Bellman-Jacobi equation, which by the verification theorem has well-behaved solutions if certain conditions on a potential are satisfied. In the case at ha...

This paper develops a general stochastic model of a frictionless security market with continuous trading. The vector price process is given by a semimartingale of a certain clr;zss, and the general stochastic integral is used to represent capital gains. Within the framework of this model, we discuss the modern theory of contingent claim valuation, including the celebrated option pricing formula...

It has often been argued that there exists an underlying biological basis of utility functions. Taking this line of argument a step further in this paper, we have aimed to computationally demonstrate the biological basis of the Black-Scholes functional form as applied to classical option pricing and hedging theory. The evolutionary optimality of the classical Black-Scholes function has been com...

We compute a sharp small-time estimate for the price of a basket call under a bi-variate SABR model with both β parameters equal to 1 and three correlation parameters, which extends the work of Bayer,Friz&Laurence[BFL14] for the multivariate Black-Scholes flat vol model. The result follows from the heat kernel on hyperbolic space for n = 3 combined with the Bellaiche[Bel81] heat kernel expansio...